The decimal representation of the number is given

Question

Q.

\sqrt{z}/4 = a.bc

The decimal representation of the number is given above, where z is a positive number and a, b and c are single-digit non-negative integers. Is a = 0?

1.  \frac{z^2}{4} > 64

2.  \frac{z^{0.25}}{4}> 2

Answer Choices

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

EgmatQuantExpert · Answer

The official solution has been posted. Looking forward to a healthy discussion..

quantumliner · Answer

Statement 1: . (z^2)/4>64
Given that z is positive, lets take the square root of both the sides, we get

z/2 >8, which can written as z >16.

Taking square root of both sides again, we get

(z^1/2) > 4, dividing both sides by 4, we get, (z^1/2)/4 > 1. So a is not equal to 0. This statement is sufficient.

Statement 2: (z^1/4)/4 > 2

Squaring both sides we get, (z^1/2)/16 > 4, this can be written as

(z^1/2)/4 > 16
. 
(z^1/2) > 64. So a is not equal to 0. This statement is sufficient.

Answer is D

EgmatQuantExpert · Answer

Official Solution

Steps 1 & 2: Understand Question and Draw Inferences

Given:

To find: Is a = 0?

Step 3: Analyze Statement 1 independently

(1) \(\frac{z^2}{4} > 64\)

Multiplying the above inequality by 4 we get:

\(z^2 > 64*4\)
Taking square roots we get

So, the answer is NO

Statement 1 is sufficient to answer the question

Step 4: Analyze Statement 2 independently

(2) \(\frac{z^{0.25}}{4}> 2\)

Since \(z^{0.25}\) is positive, squaring both sides twice will not change the sign of inequality:

So, z is not less than 16

Thus, the answer is NO

Statement 2 is sufficient to answer the question

Answer: Option D

Thanks,
Saquib
Quant Expert
e-GMAT

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IanStewart · Answer

From Statement 1, if z^2/4 > 64, then z^2 > (4)(64), and z > (2)(8), so z > 16. So √z/4 is thus greater than 1, and a cannot be zero, and Statement 1 is sufficient.

From Statement 2, z^(1/4) > 8, so z > 8^4. Then √z/4 is greater than √(8^4)/4 = 16, and the decimal representation of √z/4 cannot possibly look like "a.bc". So I have no idea how to now answer the question: is "a" the units digit in the decimal representation of √z/4? If so, then a can certainly equal zero. But if instead the question meant to say that a is the integer part of √z/4, then clearly a is greater than zero.

So it's impossible to answer the question, but the answer is A or D depending on what one guesses it means.

bumpbot · Answer

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The decimal representation of the number is given

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