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# If x and y are integers greater than 1 and x>y, what is the value of

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4863
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If x and y are integers greater than 1 and x>y, what is the value of [#permalink]

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11 Jan 2018, 23:51
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[GMAT math practice question]

If $$x$$ and $$y$$ are integers greater than $$1$$ and $$x>y$$, what is the value of $$x$$?

1) $$x+y=10$$
2) $$xy=21$$
[Reveal] Spoiler: OA

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Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink]

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12 Jan 2018, 00:04
MathRevolution wrote:
[GMAT math practice question]

If $$x$$ and $$y$$ are integers greater than $$1$$ and $$x>y$$, what is the value of $$x$$?

1) $$x+y=10$$
2) $$xy=21$$

Very similar questions:
https://gmatclub.com/forum/if-x-and-y-a ... 29055.html
https://gmatclub.com/forum/if-x-and-y-a ... 36326.html
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Joined: 30 May 2017
Posts: 42
Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink]

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12 Jan 2018, 00:10
If $$x$$ and $$y$$ are integers greater than $$1$$ and $$x>y$$, what is the value of $$x$$?

1) $$x+y=10$$
2) $$xy=21$$

Hi,

1. 7+3=10
8+2=10

insuff

BCE
2. 21=7*3*1
therefore sufficient x=7 x can't be 21 because y>1

B
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Joined: 11 Sep 2015
Posts: 2049
Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink]

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12 Jan 2018, 08:01
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Top Contributor
MathRevolution wrote:
[GMAT math practice question]

If $$x$$ and $$y$$ are integers greater than $$1$$ and $$x>y$$, what is the value of $$x$$?

1) $$x+y=10$$
2) $$xy=21$$

Target question: What is the value of x?

Given: x and y are integers greater than 1 and x > y

Statement 1: x+y=10
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 9 and y = 1. In this case, the answer to the target question is x = 9
Case b: x = 8 and y = 2. In this case, the answer to the target question is x = 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy=21
Since x and y are INTEGERS greater than 1 AND x > y, we can see that it MUST be the case that x = 7 and y = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Posts: 4863
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Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink]

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14 Jan 2018, 17:29
=>

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) and 2) together first.

Conditions 1) and 2):
$$y = 10 – x$$ and$$xy= x(10-x) = 21$$
$$⇔ -x^2 + 10x = 21$$
$$⇔ x^2 - 10x + 21 = 0$$
$$⇔ (x-3)(x-7) = 0$$
$$⇔ x = 3$$ and$$y = 7$$, or $$x = 7$$ and $$y = 3$$.
Since $$x > y$$, we must have $$x = 7$$ and $$y = 3$$.
Thus $$x = 7$$, and conditions 1) and 2) are sufficient, when taken together.

Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).

Condition 1)
There are two possible solutions: $$x = 6$$ and $$y = 4$$, and $$x = 7$$ and $$y = 3$$.
Since the solution is not unique, condition 1) is not sufficient.

Condition 2):
Either $$x = 3$$ and $$y = 7$$, or $$x = 7$$ and $$y = 3$$.
Since $$x > y, x = 7$$ and $$y = 3$$.
Thus, we have the unique solution, $$x = 7$$.
Therefore, condition 2) is sufficient.

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.

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Re: If x and y are integers greater than 1 and x>y, what is the value of   [#permalink] 14 Jan 2018, 17:29
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