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

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

Thus - Answer E

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

Let numbers be a 2a and c

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

a=3
c=5
b=6

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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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

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

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.

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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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?

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

Thanks for the explanation; my brain is not working

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

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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.

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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