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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
What is the value of x+y?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:25) correct 27% (01:33) wrong based on 62 sessions

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[GMAT math practice question]

What is the value of $$x+y$$?

1) $$x+y$$ is between $$50$$ and $$60$$
2) $$x$$ and $$y$$ are prime numbers

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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: What is the value of x+y?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the value of $$x+y$$?

1) $$x+y$$ is between $$50$$ and $$60$$
2) $$x$$ and $$y$$ are prime numbers

Obviously none of the two statements on their own are sufficient to answer.

Lets combine the two - we need two prime numbers whose sum is between 50 and 60. We could have:
x=5, y= 47, here x+y = 52
x=7, y=47, here x+y = 54

There will be other cases too, so no unique answer. Not sufficient.

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the value of x+y?  [#permalink]

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=>

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.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be 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):
$$x = 23, y = 29 : x + y = 52$$
$$x = 23, y = 31 : x + y = 54$$

Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, the answer is E.

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.
_________________ Re: What is the value of x+y?   [#permalink] 02 Mar 2018, 01:16
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