Prime # question

Question

Can someone help me with the solution for below?

A certain prime X is divided by 5 to get a fraction. Then its numerator is increased by 4 and its denominator doubled, after which the resulting fraction is reduced. The denominator of the result is odd. What is X?

a) 7
b) 5
c) 4
d) 3
e) 2

gmatnub · Answer

x = 4

I don't think this is a gmat type question, but ....

according to the question:

(x + 4) / (2 * 5)

if you reduce the denominator by 2 you get 5 (which is odd)
The question does not state whether the ratio were maintained, but I assume that it is implied.
If so, x + 4 = 2x ----> x = 4

dzelkas · Answer

4 is not prime though

jallenmorris · Answer

If you start with a few of the prime numbers, you get to the answer rather quickly. 2/5 = a fraction, 2 + 4 / 5*2 = 6/10, or 3/5 when reduced, and the denominator is odd. if x = 2, 2 is a prime number so it satisfies the rule stated in the stem.

The presumption I made was that if x = 5 or 7, then 5/5 is 1, not a fraction, and 7/5 is greater than 1, so again, not a fraction, technically speaking.

rohit929 · Answer

construct the equation (resulting fraction is reduced)
(X/5)>((X+4)/10)
solving gives X>4

Only 2 options satisfy to be odd 5 and 7 but 5/5 is not a fraction so 7 is the ans

ritula · Answer

This problem can be easily solved by substitution.
4 and 5 can be readily removed frm the list bcos 4 is not a prime no and 5 will not give us a fraction( technicaly speaking)
so that leaves us with 3 options 2,3 and 7
out of these only 2 satisfies the condition
So E is the answer

gdmat720 · Answer

Can anyone tell me how does the condition "The denominator of the result is odd" is satisfied??

jallenmorris · Answer

If a certain prime number (x) is divided by 5, the first part will have a denominator that is 5, and therefore odd. When it's doubled, like anything doubled, it will be even. The stem says that the "fraction is reduced" and results in an odd number. So that means tht 10 (divided by 5 and doubled = 10) when reduced must be an odd number. The only factors of 10 are 1, 2, 5, and 10. Of those, 1 and 5 are odd.

Since the answer is 2, when the fraction  \frac{x+4}{5*2}  is reduced, you get  \frac{3}{5}  because you start out wit 2 + 4 / 5*2, or 6 / 10. That can be reduced to 3/5 and the denominator is odd.

brokerbevo · Answer

I just tried every answer. First I got rid of any answer choices that weren't prime (C is gone). Then I did as follows:

A)  (7+4)/(5*2)  =  11/10  This is as simple as it can get and 10 is not odd
B)  (5+4)/(5*2)  =  9/10  This is as simple as it gets and 10 is not odd
D)  (3+4)/(5*2)  =  7/10  This is as simple as it gets and 10 is not odd
E)  (2+4)/(5*2)  =  6/10  =  3/5   This is the answer because 5 is odd

Prime # question

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