If the sum of 5 consecutive positive multiples of a prime number is 10

Question

If the sum of 5 consecutive positive multiples of a prime number is 105, what is the sum of the first 5 positive multiples of that prime number?

A. 30
B. 45
C. 75
D. 105
E. Can't be determined

DeLathouwer · Accepted Answer

"If the sum of 5 consecutive positive multiples of a prime number is 105, what is the sum of the first 5 positive multiples of that prime number?"

Let P be the prime number. 
In terms of equation the first part of the statement becomes: P*x + P*(x+1) + P*(x+2) + P*(x+3) + P*(x+4)=105
->P*(5x) + 10P=105
->P*(x+2)=21

There are 2 possibilities: (P,x)= (7,1) or (3,5).
(7,1) -> 7 + 14 + 21 + 28 + 35= 105
(3,5) -> 15 + 18 + 21 + 24 + 27= 105

If 7 is the prime number, the sum of the first 5 positive multiples would be 7 + 14 + 21 + 28 + 35= 105.
If 3 is the prime number, the sum of the first 5 positive multiples would be 3 + 6 + 9 + 12 + 15= 45.

-->  Answer E

pushpitkc · Answer

Since the sum of 5 consecutive positive multiples of a prime number is 105, the mean is 21. 
The numbers whose sum is 105 are 19,20,21,22,23.
Hence the prime number we are looking for is 19. 
Now, we need the sum of the first 5 positive multiples of this prime number which is not possible 
as the only positive multiples that a prime number has are the prime number and 1.

Since we need sum of first 5 positive multiples of this prime number it cannot be determined(Option E)

vibk · Answer

How I did it- Please let me know if I my thought process is incorrect

Let the prime number be p
5 consecutive multiples for p would be pa, p(a+1), p(a+2),p(a+3), p(a+4)

Sum of 5 consecutive multiples of p= 
=p 
=p  (Sum of AP)

105=p

Thus we will not be able to determine p and a using only one equation .
Hence cannot be determined

mehrotrayashraj · Answer

Hi,
Choose a prime number - 5
5 + 10+ 15 + 20 + 25 = 75 
Ans could be c

15 + 20 + 25 + 30 + 35 > 105 
10 + 15 + 20 + 25 + 30 > 105

Choose another prime number - 7
7 + 14+ 21 + 28 + 35 = 105 Ans D

Shruti0805 · Answer

Hi, Let the no. be P. As per the question, P*x + P*(x+1) + P*(x+2) + P*(x+3) + P*(x+4) = 105 --- eqn. 1 Solving the equation, we get : 5*P*x + 10*P = 105 => P*x + 2*P = 21 => P(x+2) = 21 Factors of 21 - 3,7,21 So P*(x+2)=21 can either be 7*(1+2) or 3*(1+6). Lets try the values : If x=1 and P=7, substituting in eqn. 1, we get 7+14+21+28+35 = 105 --- Satisfied but if we consider P=3 and x=6, substituting in equation leads to terms - 18+21+24+27+30 = 120 which doesn't suffice. Thus, P must be equal to 7 and x must be equal to 1. Based on these, the sum of 1st 5 multiples = 7+14+21+28+35 =105 As per me, option D should be the answer, can somebody please suggest why is it E ? Got it. :oops:

Such a careless mistake.

arvind910619 · Answer

Imo E
As we have two unknowns hence we can not determine sum of multiples .
Let the prime number be X and and Y be some positive integer .
Now according to question we have , X 
Thus we have two unknowns that can not determine answer

Sent from my ONE E1003 using  GMAT Club Forum mobile app

chetan2u · Answer

Let the prime number be x, and so sum of five positive multiples will be 
x*(y-2)+x(y-1)+xy+x(y+1)+x(y+2)=105
x(y-2+y-1+y+y+1+y+2)=105
x*5y=105......x*y=21
Since x is prime, 21 can be factored as only 7*3. Thus x can be 7 or 3.
Insufficient information

R

Gknight5603 · Answer

two sets are possible for the question.
3: 15 18 21 24 27
7: 7 14 21 28 35
 
Hence the answer is can not be determined for the provided info.

Posted from my mobile device

GMATGuruNY · Answer

Consecutive multiples constitute an EVENLY SPACED SET.
For any evenly spaced set, median = average.
Given 5 consecutive multiples that sum to 105, we get:
median = average =  \frac{sum}{count} = \frac{105}{5} =21

21 is a multiple of prime numbers 3 and 7.

Case 1: 5 consecutive multiples of 3 such that the median is 21
15, 18, 21, 24, 27 --> 15+18+21+24+27 = 105

Case 2: 5 consecutive multiples of 7 such that the median is 21
7, 14, 21, 28, 35 --> 7+14+21+28+35 = 105

The sum of the first five multiples of 3 is not equal to the sum of the first five multiples of 7.
Thus, the answer to the question stem cannot be determined.

E

If the sum of 5 consecutive positive multiples of a prime number is 10

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If the sum of 5 consecutive positive multiples of a prime number is 10

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