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What is the smallest integer that can be divided by the product of a

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New post 12 Nov 2017, 01:26
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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 12 Nov 2017, 04:16
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Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35



The integer is nothing but 7*p*p
P can be 2 at the lowest value, so 7*2*2=28
D
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 12 Nov 2017, 06:53
Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35


To get the smallest integer we need to multiply 7 with the smallest prime number, which is 2.
2*7 = 14.
Answer - B
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New post 12 Nov 2017, 06:56
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Sprincejindal wrote:
Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35


To get the smallest integer we need to multiply 7 with the smallest prime number, which is 2.
2*7 = 14.
Answer - B


thats a TRAP.
Be careful while reading Q..
Quote:
smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number

in your calculation 14/14 will leave 1 whereas Q says it should yield a prime number
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 12 Nov 2017, 07:19
Quote:
smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number


First of all can product of a prime number mean prime*1? Its the product of a prime, right?

Secondly doesn't it mean that division by 7 should yield a prime aswell? Thereby making the answer either B or E.
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New post 12 Nov 2017, 07:43
IMO, it is D. 7 x 2 x 2 = 28.
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New post 12 Nov 2017, 10:48
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chetan2u wrote:
Sprincejindal wrote:
Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35


To get the smallest integer we need to multiply 7 with the smallest prime number, which is 2.
2*7 = 14.
Answer - B


thats a TRAP.
Be careful while reading Q..
Quote:
smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number

in your calculation 14/14 will leave 1 whereas Q says it should yield a prime number


Oh yes, you are right!
So the integer is 2*2*7 and it can be divided with the product of 2*7 to yield 2, which is a prime number. Right?
Thanks!
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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 13 Nov 2017, 07:46
chetan2u wrote:
Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35



The integer is nothing but 7*p*p
P can be 2 at the lowest value, so 7*2*2=28
D


How do u know it should be p * p * 7 and not just p*7 ?

the product of a prime number and 7 means A prime number means just one NUMBER .....Like product of 7 and 8........How cn u tell that its product of p * p
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New post 13 Nov 2017, 07:52
rocko911 wrote:
chetan2u wrote:
Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35



The integer is nothing but 7*p*p
P can be 2 at the lowest value, so 7*2*2=28
D


How do u know it should be p * p * 7 and not just p*7 ?

the product of a prime number and 7 means A prime number means just one NUMBER .....Like product of 7 and 8........How cn u tell that its product of p * p



hi

Quote:
smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number


this means when you divide that integer by PRODUCT of p and 7, it should yield another prime number..
why p*p because we have to find the smallest number, so we will take p as the smallest prime number and what is remaining also as p, which should be 2
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 15 Nov 2017, 19:35
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6urra wrote:
Quote:
smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number


First of all can product of a prime number mean prime*1? Its the product of a prime, right?

Secondly doesn't it mean that division by 7 should yield a prime aswell? Thereby making the answer either B or E.



in case of first you are incorrect 1 is not Prime ,
Second you are partially correct you missed an info : the question asks for the smallest integer and 28< 35 . Hence the answer has to be D.


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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 04 Dec 2017, 14:14
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Hi All,

We're asked to find the smallest integer that can be DIVIDED by the PRODUCT of a PRIME number and 7 AND will yield a PRIME number as the result. We can answer this question by TESTing THE ANSWERS.

Since we're asked for the SMALLEST number that will fit the above information, we should start with Answer A: 7....

The smallest product that can occur between 7 and a prime is (7)(2) = 14. 7 is NOT divisibly by 14, so we can eliminate Answer A.

Answer B: 14...

While 14 is divisible by 14, the end result is 1 - but that is NOT a prime number. Eliminate Answer B.

Answer C: 24

24/14 is NOT a prime. The next two products to consider would be (7)(3) = 21 and (7)(5) = 35. However, 24/21 and 24/35 are NOT primes. Eliminate Answer C.

Answer D: 28
28/14 = 2 - and that IS a prime. This matches everything we were told, so this must be the answer.

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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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New post 11 Jan 2018, 14:46
Bunuel wrote:
What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35


Since the smallest prime number is 2, the smallest product of a prime number and 7 is 2 x 7 = 14, and the smallest integer that yields a prime number when it is divided by 14 is 28 (notice that 28/14 = 2).

Answer: D
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