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a, b, c, d satisfy a-1=b+2=c-3=d+4. Which of a, b, c, d is t

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by Max@Math Revolution » Tue Jul 09, 2019 11:19 pm

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Answers

A

B

C

D

E

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Difficulty—

[GMAT math practice question]

a, b, c, d satisfy a-1=b+2=c-3=d+4. Which of a, b, c, d is the largest?

A. a
B. b
C. c
D. d
E. all same
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by Brent@GMATPrepNow » Wed Jul 10, 2019 10:25 am
Max@Math Revolution wrote:[GMAT math practice question]

a, b, c, d satisfy a-1=b+2=c-3=d+4. Which of a, b, c, d is the largest?

A. a
B. b
C. c
D. d
E. all same
Rewrite each value in terms of the same variable.
Given: a - 1 = b + 3
Subtract 3 from both sides to get: b = a - 4

Given: a - 1 = c - 3
Add 3 to both sides to get: c = a + 2

Given: a - 1 = d + 4
Subtract 4 from both sides to get: d = a - 5

So, a, b, c and d are equal to a, a-4, a+2 and a-5 respectively.
Among the values a, a-4, a+2 and a-5, the BIGGEST is a+2

Answer: C

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Jul 11, 2019 11:36 pm
=>

Since a - 1 = b + 2, we have a - b = 3 > 0 or a > b.
Since b + 2 = c - 3, we have b = c - 5 or a - b = a - ( c - 5 ) = a - c + 5 = 3 or a - c = -2 < 0. Thus we have c > a > b.
Since c - 3 = d + 4, we have c - d = 7 and c > d.
Thus c is the largest value of a, b, c and d.

Therefore, C is the answer.
Answer: C
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