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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: 5585
GMAT 1: 800 Q59 V59
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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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12 Jan 2018, 00:51
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Difficulty:

35% (medium)

Question Stats:

65% (00:42) correct 35% (00:52) wrong based on 74 sessions

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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) $$xy=21$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Sep 2009 Posts: 46202 Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink] ### Show Tags 12 Jan 2018, 01:04 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 _________________ Intern Joined: 30 May 2017 Posts: 41 Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink] ### Show Tags 12 Jan 2018, 01:10 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 CEO Joined: 12 Sep 2015 Posts: 2563 Location: Canada Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink] ### Show Tags 12 Jan 2018, 09:01 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 Answer: B Cheers, Brent _________________ Brent Hanneson – Founder of gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5585 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x and y are integers greater than 1 and x>y, what is the value of [#permalink] ### Show Tags 14 Jan 2018, 18:29 => 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. Therefore, B 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. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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, 18:29
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