Question: The Range of Set A

Comment on The Range of Set A

This seemed very challenging to me. I understand all the concepts but seem to get stuck on data sufficiency. What level of difficulty (scoring level) would you say this question is?
gmat-admin's picture

It's a tricky one. I'd say 700+

Hi in this question when 2x+2y=40, then more than one values are possible for x and y.so range cannot be unique. So why not answer is E?
gmat-admin's picture

When we rephrase the target question, we see that the range = 2x + 2y. At this point, we don't have enough information to determine the value of 2x + 2y

However, statement 1 tells us (indirectly) that 2x + 2y = 40. So, we now have enough information. Although there are infinitely many solutions to the equation 2x + 2y = 40, we aren't required to determine the INDIVIDUAL values of x and y to answer the rephrased target question. We are only required to determine the range (which equals 2x + 2y)

gmat-admin's picture

To follow up on my last comment....IF the target question were "What is the value of x?" then statement 1 would not be sufficient. However, that is not what the target question asks.

Torkuma Teekay Gbaa's picture

Hi Brent,

I solved this question but my answer was D. Here's why...

For Statement 2, I got 7x + 3y = 72.
This lets me know that X and Y must be even numbers. So even factors of 72 that satisfy the condition 0<X<Y are 2 & 36, 4 & 18 and 6 & 12. (8 & 9 work as well but both numbers are not even and the answer for the equation is above 72) So among these numbers only 4 & 18 satisfy the equation for X & Y.

Doesn't this make Statement 2 sufficient?
gmat-admin's picture

Hi Torkuma,

There are two problems with your analysis of statement 2.

You are correct to conclude that 7x + 3y = 72
However, we cannot then conclude that x and y are both EVEN.
For example, x = 9 and y = 3 is a solution to the equation.

It's also important to point out that the question does NOT state that x and y are INTEGERS.
This means 7x + 3y = 72 can have infinitely many solutions.
For example, x = 7.2 and y = 7.2 is also a solution to the equation.

For these reasons, we cannot conclude that x = 4 and y = 18

Cheers,
Brent

I solved this question but my answer was D. Here's why...

For statement 2 : only X=3 y=17 ; satisfy the equation
gmat-admin's picture

From statement 2, we get: 7x + 3y = 72

You're correct to say that x = 3 and y = 17 is a solution to the equation 7x + 3y = 72, but there are infinitely many other solutions.

For example, x = 6 and y = 10 is another solution.
And x = 1 and y = 65/3 is a solution.
And x = 2 and y = 58/3 is a solution.
Etc.

Cheers,
Brent

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