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# Let Q represent a set of four distinct prime numbers. If the sum of

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Math Expert
Joined: 02 Sep 2009
Posts: 55715
Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 00:44
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81% (01:04) correct 19% (01:12) wrong based on 174 sessions

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Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 03:11
1
1
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

Solution -

First of all, 1 is not a prime number.

From the given information, adding four distinct numbers gives even mean those all four numbers must be even or odd. Or sum of two even or two odd numbers equals to even.

In this case, all are prime numbers. So only even prime is 2, we may not get the sum of four primes equal to even.

We have to take all odd numbers in the set i.e., 3, 5, 7, 11 to make the sum even.

The smallest odd prime number in the list is 3. ANS C
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 03:32
1
all four are prime numbers and their total is even. then all the numbers have to be odd.
smallest value of odd prime is 3 ..
so my ANS is 3 (C)
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 03:33
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

All 4 prime numbers are DISTINCT and sum of 4 prime numbers is even ----> all are ODD. (as if we include 2, then the sum = 2+3+5+7 = odd and not even!)

thus the lowest odd prime number out of the given options is 3, C is the correct answer.
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 05:27
Q = {p1,p2,p3,p4}.

Since p1+p2+p3+p4 is even, every element in Q must be odd. Hence the least possible value must be 3.

Ans (C).
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 12:15
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

Q = p1+p2+p3+p4 = even (and all primes are distinct)

if the least prime is 2 then we have sum of Q = odd....hence 2 is not possible & 1 is not prime.
next least prime is 3, this satisfies the given condition that sum of Q = even.

Ans. C. 3
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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24 Jul 2015, 12:52
1
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

Option (C) 3

-Prime numbers are distinct
- Sum of these 4 distinct prime numbers are even meaning ( odd+odd+odd+odd). Since all primes are odd except 2, meaning 2 cannot be in the set of these 4 prime numbers

Least prime number possible in this set ?
Prime numbers are 2,3,5,7.....
Since 2 cannot be in the set, the next least possible prime available will be 3

Hence Option C
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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25 Jul 2015, 13:27
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

Given: Four distinct prime numbers, with their sum is even. This means that all the digits are odd(i.e it does not contain 2, the only even prime number)

Hence the least possible value of x could be 3.

Option C
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Posts: 55715
Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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26 Jul 2015, 12:29
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

800score Official Solution:

We are told that Q is a set of four distinct prime numbers, and the sum of the numbers in Q is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.

If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of Q must be odd to yield an even sum.

Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.

The correct answer is choice (C).

Note: 1 is not a prime number.
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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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20 Nov 2016, 14:19
The critical thing to remember for this is that 1 is not a prime number.

The total of the number 2 and any other three distinct prime numbers would always be odd.

Therefore the least possible prime number to ensure an even total of four distinct prime numbers would be 3.

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Re: Let Q represent a set of four distinct prime numbers. If the sum of  [#permalink]

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31 Dec 2017, 08:47
Top Contributor
Bunuel wrote:
Let Q represent a set of four distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?

A. 1
B. 2
C. 3
D. 5
E. 7

Kudos for a correct solution.

We need to minimize the four distinct prime numbers.

We're told that the SUM of the four numbers is EVEN.
This means ALL FOUR prime numbers must be odd

ASIDE: We know this because there is only one even prime number (2). Since the four numbers are distinct, there can be, AT MOST, one 2. However, if there were one 2 (and three other odd primes), the sum of the four numbers would be ODD). So, we can conclude that the number 2 is NOT in the set of values.

So, the SMALLEST set of values is: {3, 5, 7, 11}

The number x is a member of Q, then what is the least value that x can be?

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Re: Let Q represent a set of four distinct prime numbers. If the sum of   [#permalink] 31 Dec 2017, 08:47
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