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The product X of two prime numbers is between 17 and 55. If

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The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 19 Nov 2013, 03:25
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The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =

(A) 18
(B) 29
(C) 37
(D) 44
(E) 51
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Re: The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 19 Nov 2013, 03:31
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amgelcer wrote:
The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =

(A)
18

(B)
29

(C)
37

(D)
44

(E)
51

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One of the primes is greater than 2 and less than 6. That makes it either 3 or 5. None of the options is a multiple of 5. Thus, we have to look for a multiple of 3.

Only A and E. 3*6 = 18, and 6 is not prime. Thus, answer is E, where 51 = 3*17
IMO, Sub-600 level.
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Re: The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 01 Nov 2014, 16:14
The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =

Different Approach:
a. One of the prime numbers is greater than 2 but less than 6. It implies that 3 and 5 are the one of the choice.
b. Prime number between >13 but <25 should be 17,19 and 23.

Quote:
3 5

Quote:
17 19 23


The value of X should be less than 55 hence 3*17=51 is the only choice here. Hence answer is E.
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Re: The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 04 Nov 2014, 00:48
amgelcer wrote:
The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =

(A) 18
(B) 29
(C) 37
(D) 44
(E) 51


Option B & C can be ruled out as they themselves are prime numbers

18 = 2*9 = 3*6 >> Ignore

44 = 2 * 22 = 4 * 11 >> Ignore

51 = 3*17 >> Answer

Answer = E
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Re: The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 14 Jan 2015, 10:09
I also did sth similar, but I guess sligtly different.

I used the information in the stem to do this:
17<x*y<55

2<x<6, one of them prime between 2 and 6. So, x=3 or x=5
13<y<25, one of them between 13 and 25. So, y=17 or y=19 or y=23

Then I did:
x=18/y, none of the possile values of y give a good x, reject
x=29/y, reject
x=37/y, reject
x=44/y, reject
x=51/y, x=51/3, x=17, accept. ANS E
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Re: The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 14 Jan 2015, 17:43
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Hi All,

This question is built around a variety of Number Properties, and you can use those same Number Properties to quickly get to the correct answer:

We're told a series of facts about 2 numbers:
1) They're both PRIME
2) Their PRODUCT is between 17 and 55
3) One number is between 2 and 6
4) The other number is between 13 and 25

We're asked for the product that fits these "restrictions"

First, since both numbers are PRIME and NEITHER can be "2", both numbers are ODD.
Second, (odd)(odd) = odd, so the answer MUST be ODD.
Third, the answer CANNOT be prime, since it has these 2 smaller prime numbers as factors.

So, eliminate the EVENS (Answers A and D) and the PRIMES (Answers B and C).

Final Answer:

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Re: The product X of two prime numbers is between 17 and 55. If [#permalink]

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New post 13 Mar 2018, 17:00
amgelcer wrote:
The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =

(A) 18
(B) 29
(C) 37
(D) 44
(E) 51


Since one of the prime numbers is greater than 2 but less than 6, it can be either 3 or 5.

Since the other prime number is greater than 13 but less than 25, it can be either 17, 19 or 23.

Thus, X must be 3 x 17 = 51.

Answer: E
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Re: The product X of two prime numbers is between 17 and 55. If   [#permalink] 13 Mar 2018, 17:00
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