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.
Subscribe to:
Post Comments (Atom)
Hello GMAT Hero!
ReplyDeleteYou are welcome to join us at gmatclub! Though we don't allow direct advertising or promotion on our pages, you can include your website in your signature, which will show up under each of your posts, and that's acceptable. This works well for our members - they get help from qualified experts and also brings traffic and satisfied customers to you.
Best Regards,
BB (PM me on the forum if you have any questions)
Founder of GMAT Club
http://gmatclub.com
Dear GMAT Hero,
ReplyDeleteRe: Q114 above.
If we consider (1) and (2):
Using 1, we can construct a 'finite' list of unique 8-integer sets:
[1,2,3,4,5,6,7,8]
[1,2,3,4,5,6,7,9]
....
[18,19,20,21,22,23,24,25]
Let's assume that the number of those sets is N. The probability of selecting a random 'set' is 1/N
Now for each set, we can find the probability of x<=20. Ex:
[1,2,3,4,5,6,7,8,] --> P1(x<=20) = 0
...
[18,19,20,21,22,23,24,25] --> PN(x<=20) = 3/8
Using (1) and (2) can't we calculate P(x<=20) for all sets?
P1 x 1/N
+
P2 x 1/N
+
...
+
PN * 1/N
?