If abcd ≠ 0, 0

Question

If  abcd ≠ 0 , and if  0 < c < b < a < 1 , is it true that  \frac{a^4bc}{d^2} < 1 ?

(1)  a = \sqrt{d}

(2)  d > 0

GMATinsight · Answer

Please check the explanation as attched.

Answer: Option A

https://www.youtube.com/watch?v=C471aV7584c

yashikaaggarwal · Answer

Given: ABCD ≠ 1, 0 A^4 = D^2 A^4BC/D^2 < 1 BC < 1 (since B and C both are fraction) (Sufficient) Statement 2: D>0 Case 1: D= 1 , A^4BC/D^2 < 1 Case 2: D= 2 , A^4BC/D^2 < 1 Case 3: D is in fraction, A^4BC/D^2 ≥ 1 (Insufficient) Answer is A Posted from my mobile device

IanStewart · Answer

Since d^2 is automatically positive, we can multiply the inequality in the question by d^2 on both sides, so our question becomes:

Is a^4 b c < d^2 ?

If a = √d, we can substitute for a in the question:

Is (√d)^4 bc < d^2 ?
Is d^2 bc < d^2 ?
Is bc < 1 ?

and since 0 < c < b < 1, it must be true that bc < 1, and Statement 1 is sufficient.

The sign of d is irrelevant, since we're squaring d anyway in the question, so Statement 2 isn't useful and the answer is A.

Papist · Answer

S1: a = root d can also be written as a^4 = d^2. Therefore these two terms cancel out in the above equation and the new equation is bc<1. Since we know that b and c are between 0 and 1, the product will always be less than 1. SUFFICIENT.

S2: d^2 could be smaller, larger, or equal to the numerator, which will produce different answers. NOT SUFFICIENT.

ANSWER: A

If abcd ≠ 0, 0 < c < b < a < 1, is it true that a^4bc/d^2 < 1?

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