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10 Oct 2019, 21:42
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (00:35) correct
12%
(00:34)
wrong
based on 59
sessions
History
Date
Time
Result
Not Attempted Yet
Is the product XY divisible by 22?
(1) X is divisible by 4.
(2) Y is divisible by 11.
(1) X is divisible by 4.
(2) Y is divisible by 11.
11 Oct 2019, 01:45
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Bunuel
Is the product XY divisible by 22?
(1) X is divisible by 4.
(2) Y is divisible by 11.
(1) X is divisible by 4.
(2) Y is divisible by 11.
#1
y not know insufficient
#2
x not know insufficient
from 1 &2
22= 2*11
so x being divisible by 4 will be divisible by x and y will be divisible by 11
so sufficient
yes
IMO C
11 Oct 2019, 10:14
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Bunuel
Is the product XY divisible by 22?
(1) X is divisible by 4.
(2) Y is divisible by 11.
(1) X is divisible by 4.
(2) Y is divisible by 11.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.
Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
Since X is divisible 4 and Y is divisible by 11, we can rewrite X=4a and Y=11b for some integers a and b.
We have XY =(4a)(11b)=44ab
XY is divisible by 44 and it is divisible by 22 as well.
Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condiiton 1)
If X = 4 and Y = 11, then XY = 44 is divisible by 22 and the answer is 'yes'.
If X = 4 and Y = 10, then XY = 40 is not divisible by 22 and the answer is 'no'.
Since condition 1) does not yield a unique solution, it is not suffiecient.
Condition 2)
If X = 4 and Y = 11, then XY = 44 is divisible by 22 and the answer is 'yes'.
If X = 3 and Y = 11, then XY = 33 is not divisible by 22 and the answer is 'no'.
Since condition 2) does not yield a unique solution, it is not suffiecient.
Therefore, C is the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
