Find the value of the two digit number Z?

Question

(1) The difference in the square of the digits Z is 72.

(2) Z has only four factors, two of which are prime, having a sum of 16.

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TarunKumar1234 · Answer

Find the value of the two digit number Z?

(1) The difference in the square of the digits Z is 72.

(2) Z has only four factors, two of which are prime, having a sum of 16.

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Official Answer

C

GCMEMBER · Answer

Find the value of the two digit number Z?

(1) The difference in the square of the digits Z is 72.
Z can be 39 or 93
Not sufficient

(2) Z has only four factors, two of which are prime, having a sum of 16.
Z can be 39 or 55
Not sufficient

(1) + (2)
Z = 39
Sufficient

Option C

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kntombat · Answer

Can someone help me understand how statement 1 not sufficient.
 {9}^2- {3}^2 = 72  the number has to be 93, how can be assume the number could also be 39 because 9-81=-72.

Or are we assuming  ({-9})^2 - ({-3})^2 = 72  that's why Statement 1 is insufficient.

kntombat · Answer

chetan2u ,  Bunuel ,  VeritasKarishma ,  nick1816  can someone help me with my doubt ?

chetan2u · Answer

HI

It does not say that square of tens digit - square of units digit is 72.
It just tells us that  a^2-b^2=72 . The number could be ab or ba.

KarishmaB · Answer

(1) The difference in the square of the digits Z is 72.

The square of the digits would vary from 0, 1, 4, 9 ... 64, 81. 
If the difference in the squares is 72, 81 must be one of the squares. Then the other square must be 9 because 81 - 9 = 72.
So the digits must be 3 and 9 and the number could be 39 or 93.
Not sufficient.

(2) Z has only four factors, two of which are prime, having a sum of 16.

Z will be the product of two prime factors. Sum of the primes is 16. So the possible combinations are 3*13 = 39 or 5*11 = 55. Not sufficient.

Using both, we see that Z must be 39 because only 39 satisfies both statements. 
Answer (C)

Ujjawalm8shra · Answer

Question states difference in squares of digits only, does not specify which is larger
smaller. so the number can be both 93 and 39

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Find the value of the two digit number Z?

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GMAT Data Sufficiency (DS) Questions

Find the value of the two digit number Z?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

My Rewards