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If a, b, and c are consecutive integers such that a < b < c

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If a, b, and c are consecutive integers such that a < b < c

by Brent@GMATPrepNow » Thu Jan 23, 2020 7:23 am
If a, b, and c are consecutive integers such that a < b < c, which of the following CANNOT be the value of (b² – a²)(c² – b²)?
(A) 323
(B) 483
(C) 575
(D) 613
(E) 899

Source: www.gmatprepnow.com
Difficulty level: 650 to 700
Answer: D
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Re: If a, b, and c are consecutive integers such that a < b < c

by Brent@GMATPrepNow » Fri Jan 24, 2020 8:16 am
Brent@GMATPrepNow wrote: ↑
Thu Jan 23, 2020 7:23 am
 If a, b, and c are consecutive integers such that a < b < c, which of the following CANNOT be the value of (b² – a²)(c² – b²)?
(A) 323
(B) 483
(C) 575
(D) 613
(E) 899

Source: www.gmatprepnow.com
Difficulty level: 650 to 700
Answer: D
Since a, b, and c are consecutive integers and a < b < c, we know that...
a = a
b = a + 1
c = a + 2

So, (b² – a²)(c² – b²) = [(a + 1)² - a²][(a + 2)² - (a + 1)²]
= [a² + 2a + 1 - a²][(a² + 4a + 4) - (a² + 2a + 1)]
= [2a + 1][2a + 3]
= 4a² + 8a + 3
= 4(a² + 2a) + 3
= 3 greater than some multiple of 4

Now let's check the answer choices....
(A) 323
320 is a multiple of 4, which means 323 is 3 greater than a multiple of 4
Keep A

(B) 483
480 is a multiple of 4, which means 483 is 3 greater than a multiple of 4
Keep B

(C) 575
572 is a multiple of 4, which means 575 is 3 greater than a multiple of 4
Keep C

(D) 613
610 is NOT a multiple of 4, which means 613 is NOT 3 greater than a multiple of 4
Voila!

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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