If n is the least of three different integers greater than 1, what is

Question

If n is the least of three different integers greater than 1, what is the value of n ?

(1) The product of the three integers is 90.

(2) One of the integers is twice one of the other two integers.

chetan2u · Accepted Answer

Hi..

statements..

(1) The product of the three integers is 90.  
 90=2*3*3*5 
 various combinations of 3 integers can be made 2*5*9 OR 3*5*6.. 
insuff

(2) One of the integers is twice one of the other two integers. 
 various combination.. 
2, 4,8
7,8,16
insuff

combined..
90=2*3*3*5...
 if one number is twice is DOUBLE of the other , possible case is x and 2x.. only 2 and 2*3 possible ..
so integers are 3, 5,6.. 
ans 3
suff

C

rekhabishop · Answer

The answer is C?

various combinations can be formed from 1, 
2,9,5
3,5,6
2,3,15

using 2, we see that only (3,5,6) qualifies.
hence 1+2 = C

mcm2112 · Answer

You forgot 1 more combination to statement 2 - 1,2,45 would also work.

Thus - Answer E

mehrotrayashraj · Answer

Greater than 1. You are considering 1. The answer is C.

ShivamoggaGaganhs · Answer

Let numbers be a 2a and c

2a*a*c=90
a*a *c=45

a=3
c=5
b=6

LeenaSai · Answer

Hi All , 
I am confused in this question .
It says n is the least of three different integers ... what does that mean , ——> can we infer that there are 4 integers including n .

Say , a, b, c — all are greater that 1 and n is the least of these 3 integers?

I am messed up , plz help

VeritasKarishma  ,  chetan2u

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chetan2u · Answer

No, it means there are 3 integers-n and two more. Say n, a and b. 
So we are looking for any of Two cases— 1<n<a<b or 1<n<b<a

LeenaSai · Answer

But here in the question , it is mentioned that if n is the least of three different interferes greater than 1

If I consider that n is amongst those 3 different integers then , n is lesser than n itself ??? How is this possible , am I making extra assumptions ???

Plz advice

chetan2u · Answer

By using LEAST we are not comparing two items but saying the smallest of the two. 
If I say least, it means there are 3 numbers and the one which is smallest is n. So it is not n is lesser than itself but that n is the smallest in the three number. 
On the other hand if I say n is lesser than 3 numbers. In this case we are comparing n with three other numbers.

Example 
India is the largest producer of copper. India is part of the group and is the largest producer 
India is faster growing economy than all countries in Europe. Now there is a comparison.

LeenaSai · Answer

hi chetan2u, I am thankful to you for your amazing and in dept analysis !!! You not only addressed by queries but also highlighted an important concept of comparison !!! Kudoosssss

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IloveMBA123 · Answer

What if the answer is

-3,5 and -6? this will yield 90; 3, 5 and -6 will yield 90 too, so the N can be 3 or -3? how is that sufficient?

chetan2u · Answer

It is given that integers are greater than 1, so they cannot be negative. 
Also 3, 5 and -6 will give -90 not 90.

IloveMBA123 · Answer

Thanks for the explanation; my brain is not working

BerlinDreamChaser · Answer

How to solve this question in 2 min? I need probably 4-5 min.

Posted from my mobile device

Basshead · Answer

If n is the least of three different integers greater than 1, what is the value of n ?

(1) The product of the three integers is 90.

Prime factorization of 90 =  2*3^2*5 . n could be take multiple values. INSUFFICIENT.

(2) One of the integers is twice one of the other two integers.

Clearly insufficient.

(1&2) We know the prime factorization of  90 = 2*3^2*5  and one of the integers is twice one of the other two integers. The only possibility is  3*5*6 . SUFFICIENT.

Answer is C.

ScottTargetTestPrep · Answer

Solution:
 
We need to determine the value of n given that n is the least of three distinct integers greater than 1.

Statement One Alone:
 
Since 90 = 2 x 5 x 9 = 3 x 5 x 6, we see that n can be either 2 or 3. Statement one alone is not sufficient.

Statement Two Alone:
 
This does not tell us anything about n. Statement two alone is not sufficient.

Statements One and Two Together: 
 
From statement one, we see that 90 = 2 x 5 x 9 or 90 = 3 x 5 x 6. These two multiplications are the only ways that 90 can be expressed as a product of three distinct integers each greater than 1. From statement two, we see that only for the product 3 x 5 x 6 do we have one integer that is twice another integer. Therefore, n must be 3 since it’s the least of the three integers.

Answer: C

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If n is the least of three different integers greater than 1, what is

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