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abcd ≠ 0, a:b:c = 2:3:4, c:d = 5:6, and a + b + c – d =

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abcd ≠ 0, a:b:c = 2:3:4, c:d = 5:6, and a + b + c – d =

by Max@Math Revolution » Thu May 30, 2019 12:25 am

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[GMAT math practice question]

abcd ≠ 0, a:b:c = 2:3:4, c:d = 5:6, and a + b + c - d = 42. What is the value of d?

A. 6
B. 12
C. 24
D. 36
E. 48
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by Max@Math Revolution » Sun Jun 02, 2019 4:50 pm
=>

We combine the ratios to form a single ratio for a:b:c:d as follows:
a : b : c = 2 : 3 : 4
c : d = 5 : 6

Multiplying both equations by 5 yields

a : b : c = 10 : 15 : 20
c : d = 20 : 24

and combining them to form a single ratio gives
a : b : c : d = 10 : 15 : 20 : 24

Thus, a = 10k, b = 15k, c = 20k, d = 24k for some number k.
Substituting these values into the expression for a + b + c - d yields
a + b + c - d = 10k + 15k + 20k - 24k = 21k = 42.
Thus, k = 2 and d = 24k = 48.

Therefore, the answer is E.
Answer: E
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