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Q.

If x is a positive integer less than 100 such that x is divisible by \(2^y\), where y is a positive integer, what is the value of y?

(1) \(x^2 > 3600\)

(2) \(\frac{x^2}{2^{y+2}}\) is an odd integer

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.

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If x is a positive integer less than 100 such that x is [#permalink]

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26 May 2017, 07:49

1

This post was BOOKMARKED

EgmatQuantExpert wrote:

Q.

If x is a positive integer less than 100 such that x is divisible by \(2^y\), where y is a positive integer, what is the value of y?

(1) \(x^2 > 3600\)

(2) \(\frac{x^2}{2^{y+2}}\) is an odd integer

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.

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

(1) since x >0 x>60 or 60<x<100 only x= 64 satisfies x is div. by 2^y 64= 2^6 thus y =6 88= 11*2^3 thus y=3

insuff..

(2) x can be 88 then y=2 or x=64 then y =10 insuff

combining as above ex. in (2) Ans E

Last edited by rohit8865 on 26 May 2017, 08:37, edited 2 times in total.

Re: If x is a positive integer less than 100 such that x is [#permalink]

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13 Jun 2017, 01:51

rohit8865 wrote:

EgmatQuantExpert wrote:

Q.

If x is a positive integer less than 100 such that x is divisible by \(2^y\), where y is a positive integer, what is the value of y?

(1) \(x^2 > 3600\)

(2) \(\frac{x^2}{2^{y+2}}\) is an odd integer

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.

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

(1) since x >0 x>60 or 60<x<100 only x= 64 satisfies x is div. by 2^y 64= 2^6 thus y =6 88= 11*2^3 thus y=3

insuff..

(2) x can be 88 then y=2 or x=64 then y =10 insuff

combining as above ex. in (2) Ans E

HI, Your explanation is well understood, but I have a simple query, are we not supposed to understand from the question stem that x is a multiple of 2^y?? Thanx

Re: If x is a positive integer less than 100 such that x is [#permalink]

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06 Aug 2017, 22:42

I am not sure how B is the answer. consider two examples when x=68, \frac{x^2}{2^{y+2}}, \frac{68^2}{2^{y+2}}, \frac{17*17*4*4}{2^{y+2}}, in this case to make the above value odd, y will be 2. And when x=80 \frac{x^2}{2^{y+2}} \frac{80^2}{2^{y+2}} \frac{5*5*2^4*2^4}{2^{y+2}} in this case to make the above value odd, y will be 6. there are multiple value for y. Experts please help.

(2) \(\frac{x^2}{2^{y+2}}=\frac{k^2 \times 2^{2y}}{2^{y+2}}=k^2 \times 2^{y-2}\) is odd

Hence we must have \(y-2=0 \implies y=2\). Sufficient.

The answer is B

I did almost the same but not sure what is the loophole in my method. For stat 2, (k^2* 2^2y)/(2^y*2^2) = odd => k^2* 2^2y / (2^y * 4)= odd now we multiply both sides by 4. When 4 multiplied with odd number it gives even number. so the equation becomes: k^2* 2^2y/2^y = even k^2 * 2^y = even here y can take any value and the product remains even.

for above to be odd, 2 ^ 2m = ( 2 ^(y+2)) => 2m = y + 2 => m = (y/2) + 1 also, note that y <= m (since x is divisible by 2^y), substituting for m => y <= (y+2) + 1 => y <= 2,

So y can be 1 or 2 for m = (y/2) + 1;

if y = 1, m = 1.5, but this is not possible, as m is integer if y = 2, m = 2, so we have found the value of y