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26 Nov 2018, 01:35
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:36) correct
41%
(01:40)
wrong
based on 294
sessions
History
Date
Time
Result
Not Attempted Yet
If pq/10 is an integer, is p/5 an integer?
(1) q/2 is an integer
(2) p is a prime number
M36-123
(1) q/2 is an integer
(2) p is a prime number
M36-123
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16 Nov 2021, 04:24
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Bunuel
Official Solution:
If \(p\) and \(q\) are integers and \(\frac{pq}{10}\) is an integer, is \(\frac{p}{5}\) an integer?
(1) \(\frac{q}{2}\) is an integer.
The above means that \(q\) is even.
Can \(p\) be a multiple of 5? Certainly. Consider \(p=5\) and \(q=2=even\);
Can \(p\) NOT be a multiple of 5? Certainly. Consider \(p=1\) and \(q=10=even\).
Not sufficient.
(2) \(p\) is a prime number
Can \(p\) be a multiple of 5? Certainly. Consider \(p=5=prime\) and \(q=2\);
Can \(p\) NOT be a multiple of 5? Certainly. Consider \(p=3=prime\) and \(q=10\).
Not sufficient.
(1)+(2) Examples used for (2) are also valid for (1) (because we consider even values of \(q\) there). So, even taken together we cannot answer the question. Not sufficient.
Answer: E
General Discussion
26 Nov 2018, 18:29
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Bunuel
From 1: q/2 can be any integer value >/1
so pq/10 we can say
let q= 2 so now p has to be 5 to be valid so yes p/5 is an integer
let q=10, so now p has to be 1 , so p/5 is not an integer
In suficient
From 2:
P is a prime no. it can be ,3,2,7,, so again we would get yes at 5 and no at other no. in sufficient
Again when combining let p =3 and q= 10 so pq/10 is an integer and 3/5 "p/5" is not an integer and
at p=5, q=2 , p/5 is an integer hence E ....
