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

Question

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

Sahilpandey · Answer

According to me it is d 28

Coz 7*2=14 
Here both 7 and 2 are prime and when their product which is 14 divides 28 quotient is 2 
Which is also a prime no

Sent from my iPhone using GMAT Club Forum

HARSHI2211 · Answer

let the smallest number be n . 
n has to be of the form p1*7*p2.
(n/p1*7) would result in p2 . since p1 and 7 cannot be further broken down

a.7 p1=1 ,gives result 1=(not prime) false 
b.14 p1=2 ,gives 1 not prime
c.24 not divisible by 7 
d.28 => 4x7/2x7 gives 2 => p1 & p2 =2 ,condition holds . correct answer
e.35 p1=5 ,gives 1 (not prime)

nightblade354 · Answer

2 is the smallest prime number, so we will use this because we want the smallest possible prime number; 7*2 = 14.

7/14 = Non integer
14/14 = 1 Not prime
24/14 = Non integer
28/14 = 2 Prime number! 
35/14 = Non integer

IanStewart · Answer

We want to find the smallest integer n, where

n/7p = q

and p and q are primes. So

n = 7pq

To make n as small as possible, we want to make the primes p and q as small as possible, so we want p and q to be 2, and n = 28.

pclawong · Answer

s/ 14(7*2) = prime

(A) 7/14 =X
(B) 14/14 =1 
(C) 24/14 =X
(D) 28/14 =2 
(E) 35/14 = X

Answer = D

KarishmaB · Answer

The question is fairly simple if you don't get lost in the wording of the question.

What is the smallest integer that can be divided

Dividend = N. We need the smallest possible value of N.

by the product of a prime number and 7

Divisor is say 2*7 (smallest product of prime number and 7). This should be smallest because we need the dividend to be smallest. A large divisor will need a large dividend too.

while yielding a prime number

The result should be a prime number too and since the dividend should be smallest, the result should be 2, the smallest prime number.

\frac{N}{2*7} = 2 
N = 28

Answer (D)

justdivyanshii · Answer

can anyone please help me out , in this question it says "smallest integer that can be divided by the product of a prime number" but 28 is not the product of prime numbers?

Krunaal · Answer

Read it this this way =>  smallest integer that can be divided  by  the product of   a prime number and 7

Let prime number be p,  the product of p and 7  =>  p*7

smallest integer  /  p*7  = yields a  prime number

28 = 7*2*2

let  p = 2  (a prime number)

7*2*2  /  2*7  =  2  => 2 is a prime number

We need to find  the smallest integer  which need not be a prime number necessarily, all integers except 0 and 1 can be expressed as product of prime numbers, 28 = 7*2*2. Hope it helps.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards