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# The set of prime factors of integer y has one more element than the se

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The set of prime factors of integer y has one more element than the se  [#permalink]

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11 Sep 2019, 21:10
00:00

Difficulty:

55% (hard)

Question Stats:

40% (01:35) correct 60% (01:25) wrong based on 68 sessions

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Competition Mode Question

The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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11 Sep 2019, 21:26
1
1
We are to find the least possible value from the answer choices which has one more prime factor than 84.

The idea is to start from the least value from the answer choices and move to the next higher number.

Prime factorization of 84=2^2 * 7 * 3. Hence we know that the prime factors of 84 are 2,7, and 3.

A 168 is is 2*84 hence it has the same prime factors as 84. Hence not our answer.

Next higher number option B 210
Prime factorization of 210= 2*3*5*7
As we can see, 210 has one extra prime factor which 84 doesn’t have, 5.

Hence the answer is B in my view.

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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11 Sep 2019, 21:37
Prime Factorisation of 84=7*3*2*2
So prime factors of 84 are 7,3,2^2
Since set of Prime factors of Y has one more element than 84: taking smallest Prime Factor for Y to be minimum
So additional number in prime factorisation of Y can be 2
So, Y=7*3*2*2*2=168
A
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The set of prime factors of integer y has one more element than the se  [#permalink]

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Updated on: 13 Sep 2019, 07:16
84= 2^2 x 3 x 7
Set of 84= {2, 3, 7}.......in a set, by default (unless mentioned), numbers cannot be repetitive.

Need an additional least prime factor. Next least prime number would be 5.

y = (2 x 3 x 7) x 5
=210......option B

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Originally posted by EncounterGMAT on 11 Sep 2019, 21:55.
Last edited by EncounterGMAT on 13 Sep 2019, 07:16, edited 1 time in total.
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 00:22
1
84 = 2^2 * 3 * 7
3 prime factors

Set element of Y must have 4 prime factors
A) 168 = 2^3 * 3 * 7 - 3 factors
B) 210 = 2*3*5*7 - 4 factors - the correct answer
C) 252 = 2^2 * 3^2 * 7 - 3 factors
D) 420 = 2^2 * 3 *5 * 7 - 4 factors
E) 462 = 2* 3 * 7 * 11 - 4 factors

between B, D ,E - B is the lowest value
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 00:36
The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y?

A. 168
B. 210
C. 252
D. 420
E. 462

84 can be written in prime factors as $$2^2 * 3^1 * 7^1$$
Thus total number of elements in the set of prime factors of 84 = 3 i.e {2,3 & 7}
Since y can have one more element in its set of prime factors including 2,3 and 7 it can be denoted as $$= 2^2 * 3^1 * 7^1 * 2$$
$$= 2^3 * 3^1 * 7^1$$
$$= 168$$.

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 00:55
84=2²*3*7
If Y=210=2*5*3*7
The number of factors of Y;(8) is less than the number of factors of 84;(12).
But Y has on element more than 84 and that is 5.
Option B

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The set of prime factors of integer y has one more element than the se  [#permalink]

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Updated on: 13 Sep 2019, 01:28
factors of 84 ; 2^2*3*7 ; total 3 elements
so y has 1 more element i.e least can be 5 so value of y ; 2*3*7*5 ; 210
IMO B

The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

Originally posted by Archit3110 on 12 Sep 2019, 02:21.
Last edited by Archit3110 on 13 Sep 2019, 01:28, edited 1 time in total.
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 02:40
84= 2^2*3*7
—> { 2,3,7 }
The set of prime factors of integer Y has one more element than the set of prime factors of 84:
—> {2,3,5,7}, {2,3,7,11}{2,3,7,13}... so on

In order y to be the least possible value, the set of prime factors of y must be:
—> {2,3,5,7} —> 2*3*5*7=210.

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 03:39
IMO it's A because 84 has factors 2x2x3x7
and 168 has factors 2x2x2x3x7.
One more element is a 2.
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The set of prime factors of integer y has one more element than the se  [#permalink]

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Updated on: 13 Sep 2019, 03:20
Quote:
The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

pf(84)=42,2=21,2,2={7,3,2,2}
distinct.pf(84)={7,3,2}
pf(y)={7,3,2} + one more DISTINCT prime factor (another prime {5,11,13…})
min value of (y)={7,3,2}•{smallest distinct prime: 5}=210

Originally posted by exc4libur on 12 Sep 2019, 04:36.
Last edited by exc4libur on 13 Sep 2019, 03:20, edited 1 time in total.
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 07:46
The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?
84 = 2x2x3x7
set of prime factors of 84 = {2,3,7}, number of elements in the set are 3
set of prime factors of y contains one more element than set of prime factors of 84, number of elements are 4
so, the set could be {2,3,7, 5(next minimum prime number)} or {2,3,7, 11(next prime number)}
the minimum number is = 2x3x5x7 = 210

A. 168
B. 210
C. 252
D. 420
E. 462
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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Updated on: 12 Sep 2019, 10:44
The least possible value of y corresponds to the smallest number with one more prime factor than 84. Prime factorize 84 first to find the number of prime factors in 84. 84 = 4 * 21 = 2 * 2 * 3 * 7. Therefore there are only 3 prime factors or 3 elements. Then we need to construct the smallest number with 4 prime factors, which will be 2 * 3 * 5 * 7 = 210. Therefore the answer is B.

Trap 1: Multiplying 84 by 2 doesn't give an additional factor, 2 is already a factor.

Trap 2: Multiplying 84 by 5 gives it another factor but it is not the smallest number with 4 factors.
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Originally posted by TestPrepUnlimited on 12 Sep 2019, 08:21.
Last edited by TestPrepUnlimited on 12 Sep 2019, 10:44, edited 1 time in total.
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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12 Sep 2019, 10:42
Not sure if this is a trick question which feels really easy at first look. Waiting for the OA!

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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13 Sep 2019, 03:16
Bunuel wrote:

Competition Mode Question

The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

does ONE MORE ELEMENT mean ONE MORE DISTINCT prime factor?

Thnks.
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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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13 Sep 2019, 04:09
exc4libur wrote:
Bunuel wrote:

Competition Mode Question

The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

does ONE MORE ELEMENT mean ONE MORE DISTINCT prime factor?

Thnks.

I have the same question. The question asked for "one more element" not for "one distinct prime factor".
I knew this would be a point of discussion when the answer comes out.
Highly ambiguous I feel.
Some expert comment needed.

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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13 Sep 2019, 04:54
Prasannathawait wrote:
exc4libur wrote:
Bunuel wrote:

Competition Mode Question

The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

does ONE MORE ELEMENT mean ONE MORE DISTINCT prime factor?

Thnks.

I have the same question. The question asked for "one more element" not for "one distinct prime factor".
I knew this would be a point of discussion when the answer comes out.
Highly ambiguous I feel.
Some expert comment needed.

Wordy question. Lost the correct meaning

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The set of prime factors of integer y has one more element than the se  [#permalink]

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13 Sep 2019, 10:02
exc4libur wrote:
Bunuel wrote:

Competition Mode Question

The set of prime factors of integer y has one more element than the set of prime factors of 84. What is the least possible value of y ?

A. 168
B. 210
C. 252
D. 420
E. 462

does ONE MORE ELEMENT mean ONE MORE DISTINCT prime factor?

Thnks.

yes that't the first thing that crossed my mind also. Here 5 would multiple with 84 to give 210 as least answer, if distinct factor is considered. But 168 is lesser than 210 among the given options and the way question's worded chose A instead for 2 < 5.
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The set of prime factors of integer y has one more element than the se  [#permalink]

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13 Sep 2019, 10:10
Yeah. Since distinct wasn't mentioned, even I had initially answered and chosen option A.

I think the prime number might be distinct because the question states..y has one more element THAN the set of prime factors of 84...it might be implied that any factor other than the factors of 84.

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Re: The set of prime factors of integer y has one more element than the se  [#permalink]

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13 Sep 2019, 10:18
EncounterGMAT wrote:
Yeah. Since distinct wasn't mentioned, even I had initially answered and chosen option A.

I think the prime number might be distinct because the question states..y has one more element THAN the set of prime factors of 84...it might be implied that any factor other than the factors of 84.

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I went the other way

Since set of prime factors of 84 = {2,3,7},

can't it be written as

set of prime factors of 84 = {2, 2, 3,7}

The problem arises at this point since the set can have repeat primes.

If yes then 168 s the answer otherwise B.
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Re: The set of prime factors of integer y has one more element than the se   [#permalink] 13 Sep 2019, 10:18

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