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kiran1213
Joined: 01 Dec 2017
Last visit: 24 Dec 2018
Posts: 12
Given Kudos: 24
Location: India
Schools: EDHEC (II) IE Sept18 Intake AGSM '19 (S)
GMAT 1: 520 Q42 V22
GMAT 2: 490 Q47 V13
GPA: 2.4
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (02:12) correct
58%
(01:59)
wrong
based on 163
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Not Attempted Yet
What is the total number of positive factors of a?
(1) 2a is a multiple of 50.
(2) a/9 is an integer and has exactly 3 positive factors.
(1) 2a is a multiple of 50.
(2) a/9 is an integer and has exactly 3 positive factors.
25 Dec 2018, 08:39
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What is the total number of positive factors of a?
(1) 2a is a multiple of 50.
We do not know what is 2a..
It can be 50, that is 2a=50...a=25=5^2....prime factors is (2+1)=3
Say 2a is 100, that is 2a=100....\(a=50=2*5^2\). Factors is (1+1)(2+1)=2*3=6
Insufficient.
(2) a/9 is an integer and has exactly 3 positive factors.
This means a/9 is square of a prime number..
Let \(\frac{a}{9}=9.....a=81=3^4\).. factors =(4+1)=5
Let \(\frac{a}{9}=4.....a=36=3^2*2^2\).. factors =(2+1)(2+1)=3*3=9
Different answers, so insufficient..
Combined..
a is a multiple of 25.. but \(\frac{√a}{3}\) is a prime number..
So only possible value is 25*9..
Factors of \(5^23^2\) are (2+1)(2+1)=9..
C
OA given is wrong..
(1) 2a is a multiple of 50.
We do not know what is 2a..
It can be 50, that is 2a=50...a=25=5^2....prime factors is (2+1)=3
Say 2a is 100, that is 2a=100....\(a=50=2*5^2\). Factors is (1+1)(2+1)=2*3=6
Insufficient.
(2) a/9 is an integer and has exactly 3 positive factors.
This means a/9 is square of a prime number..
Let \(\frac{a}{9}=9.....a=81=3^4\).. factors =(4+1)=5
Let \(\frac{a}{9}=4.....a=36=3^2*2^2\).. factors =(2+1)(2+1)=3*3=9
Different answers, so insufficient..
Combined..
a is a multiple of 25.. but \(\frac{√a}{3}\) is a prime number..
So only possible value is 25*9..
Factors of \(5^23^2\) are (2+1)(2+1)=9..
C
OA given is wrong..
General Discussion
Darshi04
Joined: 08 Oct 2018
Last visit: 08 Apr 2019
Posts: 55
Given Kudos: 62
Location: India
Schools: Babson '22 Stanford '22 HEC '22
GPA: 4
WE:Brand Management (Healthcare/Pharmaceuticals)
25 Dec 2018, 04:52
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kiran1213
Statement (1): 2a is a multiple of 50
Therefore a is a multiple of 50/2 = 25.
if a is a multiple of 25, a can be 25, 50, 75....so on.
Each of these numbers will have different numbers of positive factors.
Hence insufficient.
Statement (2): a/9 is an integer and has exactly 3 positive factors.
We can write this as a=9k, where k is an integer.
Or a=3^2 x k^m
It says that 'a' has exactly 3 positive factors. Therefore a=3^2 x 1 = 3^2 (because if 'k' is anything >1, then a will not have exactly 3 factors, but will have more than 3 factors)
Sufficient.
Hence, B.
I don't understand why OA is D.
