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A and B are 2-digit numbers with non-zero digits. Both digits in A are
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20 Jun 2022, 01:50
20 Jun 2022, 01:50
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A and B are 2-digit numbers with non-zero digits. Both digits in A are distinct, and B is formed by reversing the digits of A. Which of the following is always a factor of \(A^2 – B^2\)?
- A. 5
B. 15
C. 45
D. 75
E. 99
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: A and B are 2-digit numbers with non-zero digits. Both digits in A are
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20 Jun 2022, 05:28
20 Jun 2022, 05:28
1
Carcass wrote:
A and B are 2-digit numbers with non-zero digits. Both digits in A are distinct, and B is formed by reversing the digits of A. Which of the following is always a factor of \(A^2 – B^2\)?
- A. 5
B. 15
C. 45
D. 75
E. 99
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
A fast approach is to test some values of A and B
For example, it COULD be the case that A = 21 and B =12
In this case, A² - B² = 21² - 12²
= (21 + 12)(21 - 12) [aside: since 21² - 12² is a DIFFERENCE OF SQUARES, we can first factor it before evaluating it]
= (33)(9)
= (3)(11)(3)(3)
Since 5 is not a factor of (3)(11)(3)(3), we can eliminate answer choice A
Since 15 is not a factor of (3)(11)(3)(3), we can eliminate answer choice B
Since 45 is not a factor of (3)(11)(3)(3), we can eliminate answer choice C
Since 75 is not a factor of (3)(11)(3)(3), we can eliminate answer choice D
HOWEVER, 99 IS a factor of (3)(11)(3)(3). So, KEEP answer choice E
Answer: E
Cheers,
Brent
Re: A and B are 2-digit numbers with non-zero digits. Both digits in A are
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12 Apr 2024, 12:41
12 Apr 2024, 12:41
2
Algebraic approach:
let A be (10x+y), then B is (10y+x)
A^2 – B^2 = (A-B)(A+B), so
(10x+y-10y-x)(10x+y+10y+x) = (9x-9y)(11x+11y) = 9*11*(x-y)(x+y)
So there will always be a 9 and an 11 among the factors of the number. Answer E fits.
let A be (10x+y), then B is (10y+x)
A^2 – B^2 = (A-B)(A+B), so
(10x+y-10y-x)(10x+y+10y+x) = (9x-9y)(11x+11y) = 9*11*(x-y)(x+y)
So there will always be a 9 and an 11 among the factors of the number. Answer E fits.
