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Difficulty:
25%
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Question Stats:
71% (01:14) correct
29%
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If x and y are positive integers such that x^2 - y^2 = 23. What is the value of y?
A. 10
B. 11
C. 12
D. 23
E. Cannot be determined
_________________
A. 10
B. 11
C. 12
D. 23
E. Cannot be determined
_________________
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Bunuel
Explanation:
x^2 - y^2 = 23
(x+y)(x-y) = 23 X 1 (only possible value, as 23 is prime)
so, only value for x & y is 12 & 11
so, therefore, y=11
IMO-B
Given that x and y are positive integers and x^2 - y^2 = 23. And we need to find y
x^2 - y^2 = 23
=> (x-y) * (x+y) = 23 = 1*23
=> x - y = 1 ...(1)
=> x+y = 23 ...(2)
(2) - (1) we get
2y = 23-1 = 22
=> y = 11
So, Answer will be B
Hope it helps!
_________________
x^2 - y^2 = 23
=> (x-y) * (x+y) = 23 = 1*23
=> x - y = 1 ...(1)
=> x+y = 23 ...(2)
(2) - (1) we get
2y = 23-1 = 22
=> y = 11
So, Answer will be B
Hope it helps!
_________________
How to Solve :
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
MarkGMATMentor
Joined: 24 Jul 2018
Last visit: 09 Sep 2026
Posts: 80
Location: United States (CA)
GMAT 1: 790 Q51 V50
GMAT 1: 790 Q51 V50
Posts: 80
Bunuel
Alternative Approach: Backsolving
The answer choices can be easily substituted into the equation, so let's backsolve.
Start with choice A (10) because it's the easiest. If y = 10, then \(y^2 = 100\).
If x is then 11, \(x^2 = 121\), and \(121 - 100 = 21\). Not big enough.
But if x is 12, then \(x^2 = 144\), and \(144 - 100 = 44\). Too big.
However, if y = 11 and x = 12, then \(x^2 - y^2 = 144 - 121 = 23\). The answer is B.
Note that the gap between \(10^2\) and \(11^2\) is 21, and the gap between \(11^2\) and \(12^2\) is 23, an increase of 2. This pattern holds true for all squares of positive integers. The gap between squares of consecutive integers increases by 2 every time:
\(1^2 = 1\)
\(2^2 = 4\) (gap of 3)
\(3^2 = 9\) (gap of 5)
\(4^2 = 16\) (gap of 7)
etc.
Takeaways:
1. Backsolving is an effective approach on a problem like this because the answer choices can be easily substituted into the given equation.
2. Knowing the pattern for squares of consecutive integers can help you quickly zero in on the correct answer.
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