Data Sufficiency

BTGmoderatorDC wrote: ↑

Fri Jan 24, 2020 4:23 pm

For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?

(1) b, c and d are factors of a
(2) a – 2d = b + c

OA D

Source: e-GMAT

We have to ascertain whether max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))).

Let's take each statement one by one.

(1) b, c and d are factors of a

Say a > b > c > d

max(a, max(b, min(c, d))) = max(a, max(b, c)) = max(a, b) = a
max(d, max(a, min(b, c))) = max(d, max(a, b) = max(d, a) = a

The answer is Yes. Sufficient

(2) a – 2d = b + c

Since a, b, c and d are distinct positive integers, b + c is a positive number; thus a – 2d is a positive number. Thus, a > 2d and a is greatest among all.

max(a, max(b, min(c, d))) = a; and
max(d, max(a, min(b, c))) = a

The answer is Yes. Sufficient

The correct answer: D

Hope this helps!

-Jay
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