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

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

Bunuel · Answer

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

Rahul5843 · Answer

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

BrentGMATPrepNow · Answer

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

MathRevolution · Answer

=>

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

abhishekdadarwal2009 · Answer

1) 
x+y=10
x+y=10

2) 
xy=21
xy=21

Ans:

Tip:A lot of DS question go wrong if we don't read the question carefully.So, always read the question carefully in DS.

1)X+Y=10, and given X>Y,then ther are various possibilities as below
X=8 and Y=2
X=7 and Y=3
X=6 and Y=4

So option 1 Does not give any definitive answer.

2)XY=21, and given X,Y are positive. so we cant take negative values,also x,y>1 that means 21,1 and 1,21 is not considered

so we only have 3,7 and 7,3

but as we know X>Y thus x=7 and Y=3

So 2) gives definitive answer and we get B as the correct answer for this question.

Gmat2Cracker · Answer

1) x+y=10

can be many options as 
9+1
8+2
7+3
6+4
(insufficient)

2) xy=21
7*3 is only possible as x>y
(sufficient)
Answer (B)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions