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# Find the value of the two digit number Z?

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Manager
Joined: 05 Oct 2017
Posts: 65
GMAT 1: 560 Q44 V23
Find the value of the two digit number Z?  [#permalink]

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01 Oct 2018, 23:58
4
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:40) correct 48% (02:33) wrong based on 28 sessions

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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.

_________________

It’s not that I’m so smart, it’s just that I stay with problems longer. -- Albert Einstein

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Joined: 02 Aug 2009
Posts: 7334
Re: Find the value of the two digit number Z?  [#permalink]

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02 Oct 2018, 02:37
1
1
Find the value of the two digit number Z?

(1) The difference in the square of the digits Z is 72.
Let the digits be a and B, so $$a^2-b^2=72$$
Now the larger one has to be 9, so asto make a^2 as 81>72..
So b^2=81-72=9....b=3
Z can be 93 or 39
Insufficient

(2) Z has only four factors, two of which are prime, having a sum of 16.
There can be many 1,3,7,21 so 21
Or 1,5,7,35 so 35
Insufficient

Combined
Factors of 93 - 1,3,31,93... Sum of prime factors =3+31=34...NOT equal to 16
Factors of 39 - 1,3,13,39... Sum of prime factors = 3+13=16..yes
Z is 39
Sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Joined: 21 Oct 2017
Posts: 12
Re: Find the value of the two digit number Z?  [#permalink]

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02 Oct 2018, 03:37
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.

Solution :

Statement 1 is not sufficient......as Z can be 39 or 93

Statement 2 is also not sufficient .....as two prime factors can be 3 and 13 (Sum 16) or 5 and 11 (Sum 16)

Combine : Z should be 39 ...so C is the answer
Re: Find the value of the two digit number Z?   [#permalink] 02 Oct 2018, 03:37
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