QUESTION
According to medieval monks, the remains of King Arthur and Queen Guinevere were found at Glastonbury Abbey in AD 1191, and Arthur's coffin marked with the inscription (in Latin): "Here Lies Arthur, The Once and Future King."
(A) and Arthur's coffin marked with the inscription
(B) Arthur's coffin marked with the inscription
(C) and the inscription was marked on Arthur's coffin
(D) the inscription that was marked on the coffin of Arthur
(E) the coffin of Arthur had the inscription marked
Solution:
(A) is wrong. To be correct here, the passive voice would have to be used, i.e., “was marked”.
(B) is correct. The phrase acts a modifier.
(C ) is wrong. The word order is clumsy.
(D) is wrong because there is no verb in what should be a verbal phrase.
(D) is wrong. The usage is clumsy.
OG 11th Ed Q136
Joachim Raff and Giacomo Meyerbeer are examples of the kind of composer who receives popular acclaim while living, often goes into decline after death, and never regains popularity again.
(A) often goes into decline after death, and never regains popularity again
(B) whose reputation declines after death and never regains its status again
(C) but whose reputation declines after death and never regains its former status
(D) who declines in reputation after death and who never regained popularity again
(E) then has declined in reputation after death and never regained popularity
Solution:
(A) is wrong. As written it suggests that the composer goes into decline after death, but that is nonsensical. It could only be reputation that goes into decline. “again” is redundant”.
(B) is wrong. The parallel structure is erroneous. The word “whose” is incorrectly placed.
(C) is correct.
(D) is wrong. Verb tenses are confused – “regained” should be “regains”. “again” is redundant”.
(E) is wrong. Verb tenses are confused – “regained” should be “regains”.
Wednesday, May 20, 2009
Problem Solving -- Inequalities
According to many of my students, the solutions in the Official Guide (OG) are often unclear, so I will provide solutions with greater detail for certain problems in this blog.
OG 11th Ed Q114
If x is to be selected at random from set T, what is the probability that x/4 – 5 ≤ 0?
(1) T is a set of 8 integers.
(2) T is contained in the set of integers from 1 to 25, inclusive.
x/4 – 5 ≤ 0
Therefore x/4 ≤ 5.
Therefore x ≤ 20.
Consider (1). We have no information on what integers are in the set T, so it is insufficient. Eliminate A and D.
Consider (2). The set of integers from 1 to 25 is {1,2,3, …, 24, 25}. The members of set T are also in that set, but there are numerous possibilities. T could be {1,2} or it could be {19,20,21} etc. So we cannot fathom what the probability that x/4 – 5 ≤ 0 is. Insufficient. Eliminate B.
Consider (1) and (2) together. T could be for example {1,2,3,4,5,6,7,8} or {1,3,10,11, 15,16,20, 21} or {18,19,20,21,22,23,24,25} or any other set with 8 members. So there is insufficient info to find the probability requested.
The correct answer is E.
OG 11th Ed Q139
If x ≠ -y, is (x-y)/(x+y) > 1?
(1) x > 0
(2) y < 0
As I mentioned last week, a strong strategy is to pick numbers and look for a contradiction.
Consider (1). The only constraint is x>0. Try to pick numbers that demonstrate that the inequality can be either >1 or <1. x="5" y="3," x="5" y="-3,"> 1. Contradiction so (1) is insufficient. Eliminate A and D.
Consider (2). The only constraint is y<0.>1 or <1. x="-5" y="3,"> 1. When x=5 and y=-3, the inequality is (5-3)/(5+3) = ¼ < 1. Contradiction so (2) is insufficient. Eliminate B.
Consider (1) and (2). There are two constraints, x>0 and y<0. I’ll leave it to you to pick numbers and to find contradictions. Eliminate C.
The answer therefore is E.
OG 11th Ed Q114
If x is to be selected at random from set T, what is the probability that x/4 – 5 ≤ 0?
(1) T is a set of 8 integers.
(2) T is contained in the set of integers from 1 to 25, inclusive.
x/4 – 5 ≤ 0
Therefore x/4 ≤ 5.
Therefore x ≤ 20.
Consider (1). We have no information on what integers are in the set T, so it is insufficient. Eliminate A and D.
Consider (2). The set of integers from 1 to 25 is {1,2,3, …, 24, 25}. The members of set T are also in that set, but there are numerous possibilities. T could be {1,2} or it could be {19,20,21} etc. So we cannot fathom what the probability that x/4 – 5 ≤ 0 is. Insufficient. Eliminate B.
Consider (1) and (2) together. T could be for example {1,2,3,4,5,6,7,8} or {1,3,10,11, 15,16,20, 21} or {18,19,20,21,22,23,24,25} or any other set with 8 members. So there is insufficient info to find the probability requested.
The correct answer is E.
OG 11th Ed Q139
If x ≠ -y, is (x-y)/(x+y) > 1?
(1) x > 0
(2) y < 0
As I mentioned last week, a strong strategy is to pick numbers and look for a contradiction.
Consider (1). The only constraint is x>0. Try to pick numbers that demonstrate that the inequality can be either >1 or <1. x="5" y="3," x="5" y="-3,"> 1. Contradiction so (1) is insufficient. Eliminate A and D.
Consider (2). The only constraint is y<0.>1 or <1. x="-5" y="3,"> 1. When x=5 and y=-3, the inequality is (5-3)/(5+3) = ¼ < 1. Contradiction so (2) is insufficient. Eliminate B.
Consider (1) and (2). There are two constraints, x>0 and y<0. I’ll leave it to you to pick numbers and to find contradictions. Eliminate C.
The answer therefore is E.
Wednesday, May 13, 2009
3 Critical Reasoning Problems
1. Civil trials often involve great complexities that are beyond the capacities of jurors to understand. As a result, jurors' decisions in such trials are frequently incorrect. Justice would therefore be better served if the more complex trials were decided by judges rather than juries.
The argument above depends on which of the following assumptions?
(A) A majority of civil trials involve complexities that jurors are not capable of understanding.
(B) The judges who would decide complex civil trials would be better able to understand the complexities of those trials than jurors are.
(C) The judges who would preside over civil trials would disallow the most complex sorts of evidence from being introduced into those trials.
(D) Jurors' decisions are frequently incorrect even in those civil trials that do not involve great complexities.
(E) The sole reason in favor of having juries decide civil trials is the supposition that their decisions will almost always be correct.
SOLUTION:
(A) The given info includes the words “often” and “frequently”. The argument does NOT depend on “the majority”.
(B) is the correct solution.
(C ) is beyond the scope of the argument.
(D) is irrelevant to the argument, which is concerned only with complex cases.
(E) Supposition about juries’ decisions is beyond the scope of the question.
2. The only purpose for which a particular type of tape is needed is to hold certain surgical wounds closed for ten days-the maximum time such wounds need tape. Newtape is a new brand of this type of tape. Newtape's salespeople claim that Newtape will improve healing because Newtape adheres twice as long as the currently used tape does.
Which of the following statements, if true, would most seriously call into question the claim made by Newtape's salespeople?
(A) Most surgical wounds take about ten days to heal.
(B) Most surgical tape is purchased by hospitals and clinics rather than by individual surgeons.
(C) The currently used tape's adhesiveness is more than sufficient to hold wounds closed for ten days.
(D) Neither Newtape nor the currently used tape adheres well to skin that has not been cleaned.
(E) Newtape's adhesion to skin that has been coated with a special chemical preparation is only half as good as the currently used tape's adhesion to such coated skin.
SOLUTION:
(A) It is definitively stated that the maximum time wounds need tape is ten days, so it is irrelevant that most wounds take ten days to heal.
(B) Who is responsible for buying the tape is irrelevant to the claim.
(C ) is the solution
(D) Whether skin has been cleaned is irrelevant to the claim.
(E) The quality of the adhesion/stickiness is not relevant.
3. Demographers doing research for an international economics newsletter claim that the average per capita income in the country of Kuptala is substantially lower than that in the country of Bahlton. They also claim, however, that whereas poverty is relatively rare in Kuptala, over half the population of Bahlton lives in extreme poverty. At least one of the demographers' claims must, therefore, be wrong.
The argument above is most vulnerable to which of the following criticisms?
(A) It rejects an empirical claim about the average per capita incomes in the two countries without making any attempt to discredit that claim by offering additional economic evidence.
(B) It treats the vague term "poverty" as though it had a precise and universally accepted meaning.
(C) It overlooks the possibility that the number of people in the two countries who live in poverty could be the same even though the percentages of the two populations that live in poverty differ markedly.
(D) It fails to show that wealth and poverty have the same social significance in Kuptala as in Bahlton.
(E) It does not consider the possibility that incomes in Kuptala, unlike those in Bahlton, might all be very close to the country's average per capita income.
SOLUTION:
(A) Additional evidence would not be required if
(B) As long as the usage of “poverty” is consistently applied in the cases of Kuptala and Bahlton, there is no need to worry about its meaning being universally accepted.
(C) No, this criticism does not impact the argument because neither claim is about actual numbers.
(D) Social significance is irrelevant as a criticism.
(E) is the solution. Consider the distribution of incomes. In Kuptala, most could be near the mean, but in Bahlton, there are many below the mean and some far above the mean.
The argument above depends on which of the following assumptions?
(A) A majority of civil trials involve complexities that jurors are not capable of understanding.
(B) The judges who would decide complex civil trials would be better able to understand the complexities of those trials than jurors are.
(C) The judges who would preside over civil trials would disallow the most complex sorts of evidence from being introduced into those trials.
(D) Jurors' decisions are frequently incorrect even in those civil trials that do not involve great complexities.
(E) The sole reason in favor of having juries decide civil trials is the supposition that their decisions will almost always be correct.
SOLUTION:
(A) The given info includes the words “often” and “frequently”. The argument does NOT depend on “the majority”.
(B) is the correct solution.
(C ) is beyond the scope of the argument.
(D) is irrelevant to the argument, which is concerned only with complex cases.
(E) Supposition about juries’ decisions is beyond the scope of the question.
2. The only purpose for which a particular type of tape is needed is to hold certain surgical wounds closed for ten days-the maximum time such wounds need tape. Newtape is a new brand of this type of tape. Newtape's salespeople claim that Newtape will improve healing because Newtape adheres twice as long as the currently used tape does.
Which of the following statements, if true, would most seriously call into question the claim made by Newtape's salespeople?
(A) Most surgical wounds take about ten days to heal.
(B) Most surgical tape is purchased by hospitals and clinics rather than by individual surgeons.
(C) The currently used tape's adhesiveness is more than sufficient to hold wounds closed for ten days.
(D) Neither Newtape nor the currently used tape adheres well to skin that has not been cleaned.
(E) Newtape's adhesion to skin that has been coated with a special chemical preparation is only half as good as the currently used tape's adhesion to such coated skin.
SOLUTION:
(A) It is definitively stated that the maximum time wounds need tape is ten days, so it is irrelevant that most wounds take ten days to heal.
(B) Who is responsible for buying the tape is irrelevant to the claim.
(C ) is the solution
(D) Whether skin has been cleaned is irrelevant to the claim.
(E) The quality of the adhesion/stickiness is not relevant.
3. Demographers doing research for an international economics newsletter claim that the average per capita income in the country of Kuptala is substantially lower than that in the country of Bahlton. They also claim, however, that whereas poverty is relatively rare in Kuptala, over half the population of Bahlton lives in extreme poverty. At least one of the demographers' claims must, therefore, be wrong.
The argument above is most vulnerable to which of the following criticisms?
(A) It rejects an empirical claim about the average per capita incomes in the two countries without making any attempt to discredit that claim by offering additional economic evidence.
(B) It treats the vague term "poverty" as though it had a precise and universally accepted meaning.
(C) It overlooks the possibility that the number of people in the two countries who live in poverty could be the same even though the percentages of the two populations that live in poverty differ markedly.
(D) It fails to show that wealth and poverty have the same social significance in Kuptala as in Bahlton.
(E) It does not consider the possibility that incomes in Kuptala, unlike those in Bahlton, might all be very close to the country's average per capita income.
SOLUTION:
(A) Additional evidence would not be required if
(B) As long as the usage of “poverty” is consistently applied in the cases of Kuptala and Bahlton, there is no need to worry about its meaning being universally accepted.
(C) No, this criticism does not impact the argument because neither claim is about actual numbers.
(D) Social significance is irrelevant as a criticism.
(E) is the solution. Consider the distribution of incomes. In Kuptala, most could be near the mean, but in Bahlton, there are many below the mean and some far above the mean.
Monday, May 11, 2009
More data sufficiency - pick numbers carefully!
When you pick numbers, the goal is is often to find a contradiction, i.e., to show that different numbers lead to different answers. In data sufficiency, this can be an extremely effective strategy, as in the following question.
Question
If y doesn't equal 0 and y doesn’t equal -1, which is greater, x/y or x/(y+1)?
(1) x doesn’t equal 0
(2) x > y
Solution
The best approach is to pick numbers with the goal of showing there is insufficient info.
Don’t forget that you can pick negative integers and fractions.
We will have to be careful about the signs of x and y, because signs will determine which is greater.
Consider (1).
If x is 2 and y is 1, then x/y = 2, and x/(y+1) = 1. So x/y is greater.
But if x is -2 and y is 1, then x/y = -2 and x/(y+1) = -1. So x/(y+1) is greater.
There is a contradiction, so there’s insufficient info.
Eliminate A and D.
Consider (2)
Again we could have x=2 and y=1, so x/y is greater
We could not x=-2 and y=1.
However both x and y could be negative, as long as x>y.
If x= -1 and y= -2, then x/y = 1/2 , and x/(y+1) = 1, so x/(y+1) is greater.
Contradiction.
Insufficient info.
Eliminate B.
Consider (1) and (2) together.
We have already done so and found contradiction.
Not enough info.
Answer is E.
Here are two more data sufficiency problems.
Question
1. What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly 1/2 red.
(2) Each of 3 faces of C is entirely white.
Solution
Consider (1).
We don’t know what color the other faces are. They could be all red or not red at all.
So we do not know what proportion of the total surface area is red.
Eliminate A and D.
Consider (2).
Again, we don’t know what color the non-white faces are.
Eliminate B.
Consider (1) and (2) together.
Now we infer that half of three sides are red, and no part of the other three sides are white.
The fractional part that is read is half of half, a quarter.
Answer is C.
Question
S is a set of integers such that
i) if a is in S, then -a is in S, and
ii) if each of a and b is in S, then ab is in S
is -4 in S?
(1) 1 is in S
(2) 2 is in S
Solution
Consider (1).
1 is in S, so -1 is also in S.
Not enough info to determine whether -4 is in S.
Eliminate A and D.
Consider (2).
2 is in S, so -2 is also in S.
2 and -2 are both members of S, so their product,-4, must be in S according to (ii).
Sufficient info.
Answer is B.
Question
If y doesn't equal 0 and y doesn’t equal -1, which is greater, x/y or x/(y+1)?
(1) x doesn’t equal 0
(2) x > y
Solution
The best approach is to pick numbers with the goal of showing there is insufficient info.
Don’t forget that you can pick negative integers and fractions.
We will have to be careful about the signs of x and y, because signs will determine which is greater.
Consider (1).
If x is 2 and y is 1, then x/y = 2, and x/(y+1) = 1. So x/y is greater.
But if x is -2 and y is 1, then x/y = -2 and x/(y+1) = -1. So x/(y+1) is greater.
There is a contradiction, so there’s insufficient info.
Eliminate A and D.
Consider (2)
Again we could have x=2 and y=1, so x/y is greater
We could not x=-2 and y=1.
However both x and y could be negative, as long as x>y.
If x= -1 and y= -2, then x/y = 1/2 , and x/(y+1) = 1, so x/(y+1) is greater.
Contradiction.
Insufficient info.
Eliminate B.
Consider (1) and (2) together.
We have already done so and found contradiction.
Not enough info.
Answer is E.
Here are two more data sufficiency problems.
Question
1. What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly 1/2 red.
(2) Each of 3 faces of C is entirely white.
Solution
Consider (1).
We don’t know what color the other faces are. They could be all red or not red at all.
So we do not know what proportion of the total surface area is red.
Eliminate A and D.
Consider (2).
Again, we don’t know what color the non-white faces are.
Eliminate B.
Consider (1) and (2) together.
Now we infer that half of three sides are red, and no part of the other three sides are white.
The fractional part that is read is half of half, a quarter.
Answer is C.
Question
S is a set of integers such that
i) if a is in S, then -a is in S, and
ii) if each of a and b is in S, then ab is in S
is -4 in S?
(1) 1 is in S
(2) 2 is in S
Solution
Consider (1).
1 is in S, so -1 is also in S.
Not enough info to determine whether -4 is in S.
Eliminate A and D.
Consider (2).
2 is in S, so -2 is also in S.
2 and -2 are both members of S, so their product,-4, must be in S according to (ii).
Sufficient info.
Answer is B.
Saturday, May 9, 2009
RTQ - Read the Question!
In the GMAT, it is essential to RTQ (read the question) very carefully.
Today, in considering two data sufficiency questions, we'll come across an extremely sneaky problem that demands you must do exactly that.
Question 1.
Is X^2 equal to XY?
(1) X^2 - Y^2 = (X+5)(Y-5)
(2) X = Y
Solution:
Consider the given info.
If X^2 = XY, then X=Y as long as X is not equal to 0.
Consider (1).
Expanding right side, we obtain:
X^2 - Y^2 = XY -5X +5Y -25.
Rearranging, X^2 -XY = Y^2 -5X +5Y -25
X^2 = XY iff and only if X^2 - XY = 0,
that is, if Y^2 -5X +5Y -25 = 0.
But there are no constraints on what values X and Y can take, so we cannot determine what Y^2 -5X +5Y -25 is equal to.
Not sufficient info.
Eliminate A and D.
Consider (2)
X=Y implies that XY = X^2.
Sufficient.
Answer is B.
Question 2.
A jewelry dealer initially offered a bracelet for sale at an asking price that would give a profit to the dealer of 40% of the original cost. What was the original cost of the bracelet?
(1) After reducing this asking price by 10%, the jewelry dealer sold the bracelet at a profit of $403.
(2) The jeweler sold the bracelet for $1953.
Consider question stem.
Let original cost = C.
Therefore, profit = 0.4C, and price = 1.4C.
These will be critical when considering (1) and (2).
Consider (1)
Price is reduced by 10%.
10% of 1.4C is 0.14C.
So new price is 1.26C.
Profir is now 0.26C.
0.26C= 403, so C = 403/0.26, which you don’t need to calculate.
(1) is sufficient
Consider (2)
We do not know if the actual selling price is the same as the initial offer price. So we do not know if it is valid to say that 1.4C = 1953.
(2) is not sufficient.
This is a very sneaky question, which demonstrates that you have to RTQ very carefully.
Answer is A.
Today, in considering two data sufficiency questions, we'll come across an extremely sneaky problem that demands you must do exactly that.
Question 1.
Is X^2 equal to XY?
(1) X^2 - Y^2 = (X+5)(Y-5)
(2) X = Y
Solution:
Consider the given info.
If X^2 = XY, then X=Y as long as X is not equal to 0.
Consider (1).
Expanding right side, we obtain:
X^2 - Y^2 = XY -5X +5Y -25.
Rearranging, X^2 -XY = Y^2 -5X +5Y -25
X^2 = XY iff and only if X^2 - XY = 0,
that is, if Y^2 -5X +5Y -25 = 0.
But there are no constraints on what values X and Y can take, so we cannot determine what Y^2 -5X +5Y -25 is equal to.
Not sufficient info.
Eliminate A and D.
Consider (2)
X=Y implies that XY = X^2.
Sufficient.
Answer is B.
Question 2.
A jewelry dealer initially offered a bracelet for sale at an asking price that would give a profit to the dealer of 40% of the original cost. What was the original cost of the bracelet?
(1) After reducing this asking price by 10%, the jewelry dealer sold the bracelet at a profit of $403.
(2) The jeweler sold the bracelet for $1953.
Consider question stem.
Let original cost = C.
Therefore, profit = 0.4C, and price = 1.4C.
These will be critical when considering (1) and (2).
Consider (1)
Price is reduced by 10%.
10% of 1.4C is 0.14C.
So new price is 1.26C.
Profir is now 0.26C.
0.26C= 403, so C = 403/0.26, which you don’t need to calculate.
(1) is sufficient
Consider (2)
We do not know if the actual selling price is the same as the initial offer price. So we do not know if it is valid to say that 1.4C = 1953.
(2) is not sufficient.
This is a very sneaky question, which demonstrates that you have to RTQ very carefully.
Answer is A.
Thursday, May 7, 2009
4 Challenging Sentence Correction Problems
Problem involves S-V agreement, Countable noun, Idiom.
Because paper of all kinds is the biggest single component of municipal trash, many municipalities have tried recycling to reduce the cost of trash disposal.
(a) Because paper of all kinds is the biggest single component of municipal trash, many municipalities have tried recycling to reduce the cost of trash disposal.
(b)Because paper of all kinds is the biggest single component in municipal trash, many municipalities tried to recycle so that the cost of trash disposal is reduced.
(c) Because paper of all kinds are the biggest single components of municipal trash, many municipalities have tried to recycle to reduce the cost of trash disposal.
(d) All kinds of paper are the biggest single components of municipal trash, and so many municipalities have tried recycling to reduce the cost of trash disposal.
(e) All kinds of paper is the biggest single component of municipal trash, so many municipalities have tried to recycle so that the cost of trash disposal could be reduced
Solution:
Paper is an uncountable noun, so S-V agreement requires “is” not “are.” Eliminate (c).
“Component of” not “in” is idiomatically correct. Eliminate (b).
“All kinds of paper” is an awkward phrase so eliminate (d) and (e).
The remaining choice (a) is correct.
Problem involves S-V agreement problem
Migraine, the most debilitating common form of headache, afflicts perhaps 18 million Americans, who collectively lose 64 million workdays a year, and they cost the nation $50 billion in medical expenses and lost work time .
(A) year, and they cost the nation $50 billion in medical expenses and lost
(b) year and thus cost the nation $50 billion in medical expenses and lost
(c) year, so as to cost the nation $50 billion in medical expenses and lost
(d) year that costs the nation $50 billion in lost medical expenses and
(e) year, which thus cost the nation $50 billion in lost medical expenses and
Solution:
In SC problems, it helps to rephrase the non-underlined phrase in as a simple terms as possible. Here we have:
Migraine afflicts 18 million Americans, who lose 64 million workdays a year, …
By noticing that “who lose 64 million workdays a year” is parenthetical, it becomes clear that it is Americans that cost the nation $50 billion.
(d) and (e) are wrong because they imply that it is the year that costs $50 billion.
(a) carries the correct sense and meaning but is more awkward than (b) and does not carry the implication sense that “thus” carries.
“so as to” is an awkward expression that is rarely correct on the GMAT, and is wrong here.
Also (d) and (e) are wrong because they imply that the medical expenses were lost.
The answer is (b).
Problem involves S-V agreement, Passive Voice, Idioms
13) Foreign investors, because of their growing confidence in their capability for making profitable investments in the United States, have been led to move from passive involvement in commercial real estate partnerships to active development of their own increasingly ambitious projects.
(a) Foreign investors, because of their growing confidence in their capability for making profitable investments in the United States, have been led
(b) Foreign investors, growing confident about their capability for making profitable investments in the United States, has led them
(c) Growing confidence in their ability to make profitable investments in the United States has led foreign investors
(d) Growing confidence in their ability for making profitable investments in the United States have led foreign investors
(e) Growing confident about their capabilities for making profitable investments in the United States, foreign investors have been led
Usage of the passive “have been led” does not make sense in (a) and (e).
“Foreign investors has” is an S-V agreement error. Eliminate (b).
“ability for doing” is idiomatically wrong. Eliminate (d).
The correct answer is (c)
Problem involves Modifiers, Like vs As.
Unlike other arachnids, which have their nerve cells evenly distributed along their
bodies, the scorpion's nerve cells are clustered in its head, like a mammal's.
(a) bodies, the scorpion's nerve cells are clustered in ~ its head, like a mammal's
(b) bodies, the scorpion's head has a cluster of nerve cells, as a mammal does
(c) body, the scorpion has a cluster of nerve cells in its head, as a mammal does
(d) body, nerve cells are clustered in the scorpion's head, like a mammal's
(e) body, a cluster of nerve cells is in the scorpion's head, like a mammal's
Solution
The easiest way to solve this problem is by examining the modifier.
Consider the sentence without the parenthetical “which … body/bodies” phrase.
The word following “unlike other arachnids,” must be the name of another arachnid, and not the name of a body part.
Answer (c) is the only one that satisfies. It is the correct answer.
Also, not that in (c), “as a mammal does” is correct because “as” is followed by a verb phrase.
Because paper of all kinds is the biggest single component of municipal trash, many municipalities have tried recycling to reduce the cost of trash disposal.
(a) Because paper of all kinds is the biggest single component of municipal trash, many municipalities have tried recycling to reduce the cost of trash disposal.
(b)Because paper of all kinds is the biggest single component in municipal trash, many municipalities tried to recycle so that the cost of trash disposal is reduced.
(c) Because paper of all kinds are the biggest single components of municipal trash, many municipalities have tried to recycle to reduce the cost of trash disposal.
(d) All kinds of paper are the biggest single components of municipal trash, and so many municipalities have tried recycling to reduce the cost of trash disposal.
(e) All kinds of paper is the biggest single component of municipal trash, so many municipalities have tried to recycle so that the cost of trash disposal could be reduced
Solution:
Paper is an uncountable noun, so S-V agreement requires “is” not “are.” Eliminate (c).
“Component of” not “in” is idiomatically correct. Eliminate (b).
“All kinds of paper” is an awkward phrase so eliminate (d) and (e).
The remaining choice (a) is correct.
Problem involves S-V agreement problem
Migraine, the most debilitating common form of headache, afflicts perhaps 18 million Americans, who collectively lose 64 million workdays a year, and they cost the nation $50 billion in medical expenses and lost work time .
(A) year, and they cost the nation $50 billion in medical expenses and lost
(b) year and thus cost the nation $50 billion in medical expenses and lost
(c) year, so as to cost the nation $50 billion in medical expenses and lost
(d) year that costs the nation $50 billion in lost medical expenses and
(e) year, which thus cost the nation $50 billion in lost medical expenses and
Solution:
In SC problems, it helps to rephrase the non-underlined phrase in as a simple terms as possible. Here we have:
Migraine afflicts 18 million Americans, who lose 64 million workdays a year, …
By noticing that “who lose 64 million workdays a year” is parenthetical, it becomes clear that it is Americans that cost the nation $50 billion.
(d) and (e) are wrong because they imply that it is the year that costs $50 billion.
(a) carries the correct sense and meaning but is more awkward than (b) and does not carry the implication sense that “thus” carries.
“so as to” is an awkward expression that is rarely correct on the GMAT, and is wrong here.
Also (d) and (e) are wrong because they imply that the medical expenses were lost.
The answer is (b).
Problem involves S-V agreement, Passive Voice, Idioms
13) Foreign investors, because of their growing confidence in their capability for making profitable investments in the United States, have been led to move from passive involvement in commercial real estate partnerships to active development of their own increasingly ambitious projects.
(a) Foreign investors, because of their growing confidence in their capability for making profitable investments in the United States, have been led
(b) Foreign investors, growing confident about their capability for making profitable investments in the United States, has led them
(c) Growing confidence in their ability to make profitable investments in the United States has led foreign investors
(d) Growing confidence in their ability for making profitable investments in the United States have led foreign investors
(e) Growing confident about their capabilities for making profitable investments in the United States, foreign investors have been led
Usage of the passive “have been led” does not make sense in (a) and (e).
“Foreign investors has” is an S-V agreement error. Eliminate (b).
“ability for doing” is idiomatically wrong. Eliminate (d).
The correct answer is (c)
Problem involves Modifiers, Like vs As.
Unlike other arachnids, which have their nerve cells evenly distributed along their
bodies, the scorpion's nerve cells are clustered in its head, like a mammal's.
(a) bodies, the scorpion's nerve cells are clustered in ~ its head, like a mammal's
(b) bodies, the scorpion's head has a cluster of nerve cells, as a mammal does
(c) body, the scorpion has a cluster of nerve cells in its head, as a mammal does
(d) body, nerve cells are clustered in the scorpion's head, like a mammal's
(e) body, a cluster of nerve cells is in the scorpion's head, like a mammal's
Solution
The easiest way to solve this problem is by examining the modifier.
Consider the sentence without the parenthetical “which … body/bodies” phrase.
The word following “unlike other arachnids,” must be the name of another arachnid, and not the name of a body part.
Answer (c) is the only one that satisfies. It is the correct answer.
Also, not that in (c), “as a mammal does” is correct because “as” is followed by a verb phrase.
More Math Problem Solving
Logistic Growth Problem
On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125?
a. 40
b. 100
c. 400
d. 1,000
e. 10,000
Solution:
The increase form 125 to 165 is 40, which is 4 increments of 10.
So there are four tenfold increases, that is 10 to the power 4 = 10,000
Answer choice (e).
This kind of problem also appears in the Official Guide 10th Edition. Incidentally this is the concept behind logarithms, but don’t worry – logs are not on the GMAT.
Readers may be familiar with the Richter Scale for earthquake intensity. When the measurement increases by 1, the intensity increases by 10. For example, an earthquake of 7 on the Richter Scale is 100 times more intense than an earthquake of 5 on the Richter Scale.
Algebra and Arithmetic Problem in Geometry Disguise
The volume of a sphere with radius r is (4πr^3) /3 and the surface area is 4πr^2. If a spherical balloon has a volume of 972π cubic centimeters, what is the surface area of the balloon in square centimeters?
324
729
243π
324π
729π
At first glance this appears to be a geometry problem but at closer inspection it is a straightforward algebra problem.
To find the surface area SA, we need the radius r.
We can find r because we know what V is, and how it is related to r.
V=972π = (4πr^3) /3
It might appear that you’ll have to do a lot of arithmetic either mentally or on paper, but cancelling shouldn' make it too hard.
Find r^3in terms of V:
r^3=3V/4π
Here r^3 = 3*972 π/4 π
Cancelling, we obtain r^3 = 3*243 = 729
The GMAT Hero method recommends that you learn by heart the list of squares and cubes of numbers up to 12, jsut as you (should) have learned multiplication tables at primary school.
You should recognize that 9^3=729.
So r = 9.
Plug that into the given formula for surface area,
SA = 4π(9^2) = 4(81) π
SA = 324 π
Answer choice (d).
The main difficulty with this problem is finding the cube root of 729.
Percentage Problem
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?
$600
$800
$1,000
$1,600
$2,400
Initially it may appear that not enough information is given, but keep calm – you can do this!
The difference between $60 and $40 is $20, so the 10 rooms would have $20x10 = $200 value.
From the info given, $200 is the 25% reduction from the actual total (call it T)
Algebraically, 200 = 0.25T
So T = 200/0.25 = 800
Answer choice (b).
On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125?
a. 40
b. 100
c. 400
d. 1,000
e. 10,000
Solution:
The increase form 125 to 165 is 40, which is 4 increments of 10.
So there are four tenfold increases, that is 10 to the power 4 = 10,000
Answer choice (e).
This kind of problem also appears in the Official Guide 10th Edition. Incidentally this is the concept behind logarithms, but don’t worry – logs are not on the GMAT.
Readers may be familiar with the Richter Scale for earthquake intensity. When the measurement increases by 1, the intensity increases by 10. For example, an earthquake of 7 on the Richter Scale is 100 times more intense than an earthquake of 5 on the Richter Scale.
Algebra and Arithmetic Problem in Geometry Disguise
The volume of a sphere with radius r is (4πr^3) /3 and the surface area is 4πr^2. If a spherical balloon has a volume of 972π cubic centimeters, what is the surface area of the balloon in square centimeters?
324
729
243π
324π
729π
At first glance this appears to be a geometry problem but at closer inspection it is a straightforward algebra problem.
To find the surface area SA, we need the radius r.
We can find r because we know what V is, and how it is related to r.
V=972π = (4πr^3) /3
It might appear that you’ll have to do a lot of arithmetic either mentally or on paper, but cancelling shouldn' make it too hard.
Find r^3in terms of V:
r^3=3V/4π
Here r^3 = 3*972 π/4 π
Cancelling, we obtain r^3 = 3*243 = 729
The GMAT Hero method recommends that you learn by heart the list of squares and cubes of numbers up to 12, jsut as you (should) have learned multiplication tables at primary school.
You should recognize that 9^3=729.
So r = 9.
Plug that into the given formula for surface area,
SA = 4π(9^2) = 4(81) π
SA = 324 π
Answer choice (d).
The main difficulty with this problem is finding the cube root of 729.
Percentage Problem
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?
$600
$800
$1,000
$1,600
$2,400
Initially it may appear that not enough information is given, but keep calm – you can do this!
The difference between $60 and $40 is $20, so the 10 rooms would have $20x10 = $200 value.
From the info given, $200 is the 25% reduction from the actual total (call it T)
Algebraically, 200 = 0.25T
So T = 200/0.25 = 800
Answer choice (b).
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