If x^2

Question

If  x^2 < 81  and  y^2 < 25 , what is the largest prime number that can be equal to  x - 2y ?

A. 3
B. 7
C. 11
D. 13
E. 17

Bunuel · Accepted Answer

Official Solution:

If  x^2 < 81  and  y^2 < 25 , what is the largest prime number that can be equal to  x - 2y ?

A. 3
B. 7
C. 11
D. 13
E. 17

It is important to note that we are not given that  x  and  y  are integers.
 
 x^2 < 81  implies that  -9 < x < 9 , and  y^2 < 25  implies that  -5 < y < 5 . Now, since the largest value of  x  is slightly less than 9 and the largest value of  -2y  is slightly less than 10 (for instance, if  y=-4.9 ), the largest value of  x - 2y  is slightly less than  9 + 10 = 19 . This means that the largest prime number that can be equal to  x - 2y  is 17. For example, if  x = 8  and  y = -4.5 , then  x - 2y = 17 .

Answer: E

Arro44 · Answer

I overlooked that the numbers do not have to be intergers, therefore the following would work:

x= 8.9 , y = -4.9

x-2y = 8.9 - (-9.8) = 18.7

Hence choice E is the biggest prime

dimmak · Answer

My approach is the following:

We need the greatest prime number, so we have to maximize x-2y, how? y has to be negative

So then:

\(x^{2}<9^{2}\) ---> x = 9
\(y^{2}<(-5)^{2}\) ---> y = -5

Limit = 9 + 10 = 19 prime but we can't take it, we need a prime less than 19

If we take one digit less we have that:

\(x^{2}=8^{2}\) ---> x = 8
\(y^{2}=(-4)^{2}\) ---> y = -4

So then 8 + 8 =16 not prime

There are two numbers between 16 and 19 --> 17 (prime) and 18 (not prime)

Answer E

niks18 · Answer

Algebraic approach - x^2<81 => -9 -5

chetan2u · Answer

x^2<81.......|x|<9.........x>-9...and...x<9 y^2<25.......|y|<5.........y>-5.... and.... y<5 ..... the MAX value of x-2y is when x is positive and y is negative so just LESS than 9-2*(-5)=9+10=19 so <19 therefore x-2y can take ANY value <19... 17 is the closest prime number to 19, hence answer 17 E

gmatpro15 · Answer

x<9
y<5

For number to be largest 
x-2y

we need to have x has +ve and y should be -ve

9-2(-5) = 19
but it should be less than 19

so 9-2(-4) = 17
answer E

SergejK · Answer

Bunuel : Is the fact that we are not dealing with integers the reason that we don't have to do this additional step: -8<=x<=8 and -8<= -2y<=8?

Bunuel · Answer

______________________________
Yes.

ManishaPrepMinds · Answer

If x^2 < 81 and y^2 < 25, what is the largest prime that can be equal to x – 2y?
A. 7
B. 11
C. 13
D. 17
E. 19

Correct Answer: D (17) 
 Common Trap Answers: E(19) & C(13)

The Traps:

1. Strict Inequalities Are Misinterpreted

The given constraints are:
x^2 < 81 → so -9 < x < 9
 y^2 < 25 → so -5 < y < 5

Many test-takers  mistakenly treat these as inclusive  (i.e., ≤) and assume values like x=9 or y=−5 are valid.
But since the inequalities are strict (“<”), boundary values like 9 or -5  are not allowed .
 Hence, a value like x−2y=19 is  not possible , even though many pick it, thinking it is.
 
 This is a classic GMAT trap — misreading strict vs. inclusive inequalities leads to incorrect range assumptions.

2.  Students Assume Integer-Only Values

Even if students understand the bounds, they often test only integer values of x and y.
 For example:
 x = 8, y = -4 → x - 2y = 8 + 8 = 16, and then incorrectly pick 13 as the highest prime < 16. So they pick option C. 
 
 But this ignores that  x and y can be real numbers  (e.g., x=8,y=−4.5), and 17 is valid.

This is another layer of the trap: assuming integers when not required.

Range Analysis  :

To better understand, try testing extremes:

x  
  y  
  x - 2y  
 
   -9  
  -5  
  -9 + 10 = 1  
 
   -9  
  5  
  -9 - 10 = -19  
 
   9  
  -5  
  9 + 10 = 19 ❌ (not allowed)  
 
   9  
  5  
  9 - 10 = -1

So, valid x – 2y values are in (-19, 19) → 17 is possible and is the highest prime in this range.

Key Takeaways:

Don’t assume variables are integers unless explicitly stated 
 Strict inequalities (< or >) exclude boundary values 
 Use upper/lower bound logic or a table to test ranges 
 Be alert to  trap answers  derived from integer assumptions or inclusive boundaries

SilviaLorena · Answer

But the equation tells us less than, not less than or equal to. 
Since 
x2 less than 81,
8(8) less than 81

or?

Bunuel · Answer

Yes, the inequalities are strict, so x cannot be 9 and y cannot be 5 or -5.

But we do not need those boundary values. For example, x = 8 is allowed because 8^2 < 81, and y = -4.5 is allowed because (-4.5)^2 < 25.

Then x - 2y = 8 - 2(-4.5) = 17.

So 17 is possible even with the strict “less than” signs.

If x^2<81 and y^2<25, what is the largest prime number that can be equ

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My Rewards

x	y	x - 2y
-9	-5	-9 + 10 = 1
-9	5	-9 - 10 = -19
9	-5	9 + 10 = 19 ❌ (not allowed)
9	5	9 - 10 = -1

GMAT Problem Solving (PS) Questions