Number Properties

Question

If p is a positive integer and 10p/96 is an integer, then the minimum number of  unique  prime factors p could have is:

A. 1
B. 2
C. 3
D. 4
E. 5

B

I'm trying to build a case for A, any opinions?

lagomez · Answer

How did you get 1?

Just set P = 96

TheSituation · Answer

I just took another look at the OE after taking a break for a few hours.

I honestly don't know how it didn't make sense before. I read it and it clicked, just made sense instantly.

For me, this is the most frustrating part of my GMAT prep. After MONTHS of studying quant heavily I will still make stupid mistakes like that. Careless, silly mistakes.

lagomez · Answer

happens to all of us

bibha · Answer

What is the OA? Isn't it B?

oldstudent · Answer

The OA is B. 10p/96= 5.2.p/3.2^5 => For 10p/96 to be an integer p should have factors 3, 2^4, so that it gets divided by denominator without leaving any remainder. As the question asks "unique" prime factors-> they are 3 and 2 -> so 2 ->B

whiplash2411 · Answer

For a problem like this, plugging in might not necessarily work. You need to narrow down the fraction to simplest possible one and then find prime factors of the denominator to figure this out.

\frac{10p}{96} = \frac{5p}{48}

48 = 2*24 = 2*2*12 = 2*2*2*6 = 2*2*2*2*3 = 2^4*3

Thus there are AT least two prime factors to p.

ezhilkumarank · Answer

My attempt:

10p/96 should resolve to a integer => 5p/48 should resolve to an integer.

Hence p/48 should resolve to a integer.

48 -- > 2^4 * 3.

Hence p should have atleast 2^4*3 for p/48 to resolve to a int.

The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).

helenec · Answer

If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is:

1. first you need to reduce the fraction -> 5p/48 int

2. then prime factor the denominator: 48 = 4*2*2*3 = 2^4*3

3. you can see that there is no 5 in denominator so p needs to have at least 2^4*3 to be a multiple of 48

4. notice that if denominator had a 5 -> one 5 would be cancelled

Number Properties

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