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There is a set of 10 consecutive integers. If the sum of the largest 5

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There is a set of 10 consecutive integers. If the sum of the largest 5  [#permalink]

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New post 25 Dec 2018, 13:14
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:17) correct 27% (01:40) wrong based on 30 sessions

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There is a set of 10 consecutive integers. If the sum of the largest 5 integers in the set is 355, what is the sum of the smallest 5 integers?

a. 315
b. 320
c. 325
d. 330
e. 355
VP
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There is a set of 10 consecutive integers. If the sum of the largest 5  [#permalink]

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New post 25 Dec 2018, 14:54
Jazzmin wrote:
There is a set of 10 consecutive integers. If the sum of the largest 5 integers in the set is 355, what is the sum of the smallest 5 integers?

a. 315
b. 320
c. 325
d. 330
e. 355


terms 1-5 are each 5 less than terms 6-10 respectively
355-5*5=330
D
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Re: There is a set of 10 consecutive integers. If the sum of the largest 5  [#permalink]

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New post 26 Dec 2018, 09:53

Solution



Given:
    • There is a set of 10 consecutive integers
    • The sum of the largest 5 integers in the set is 355

To find:
    • The sum of the smallest 5 integers

Approach and Working:
As all the 10 numbers are consecutive integers, we can say:
    • 6th number – 1st number = 5
    • 7th number – 2nd number = 5
    • 8th number – 3rd number = 5
    • 9th number – 4th number = 5
    • 10th number – 5th number = 5

Therefore, sum of last 5 numbers – sum of first 5 numbers = 5 x 5 = 25
Or, sum of first 5 numbers = sum of smallest 5 numbers = 355 – 25 = 330

Hence, the correct answer is option D.

Answer: D

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Re: There is a set of 10 consecutive integers. If the sum of the largest 5  [#permalink]

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New post 26 Dec 2018, 12:40
Jazzmin wrote:
There is a set of 10 consecutive integers. If the sum of the largest 5 integers in the set is 355, what is the sum of the smallest 5 integers?

a. 315
b. 320
c. 325
d. 330
e. 355


Consecutive integers***

Sum of largest 5 integers = 335.

If we divide 335 by 5 we will get the 8th one:

335/5 = 71

8th = 71.

So, 5th =68.

4th = 67
3rd=66
2nd= 65
1st = 64.

Add them:

68 + 67 + 66 + 65 + 64 = 330.

D is the correct answer.
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Re: There is a set of 10 consecutive integers. If the sum of the largest 5  [#permalink]

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New post 26 Dec 2018, 16:00
Jazzmin wrote:
There is a set of 10 consecutive integers. If the sum of the largest 5 integers in the set is 355, what is the sum of the smallest 5 integers?

a. 315
b. 320
c. 325
d. 330
e. 355



let 1st term be x
since all are consective so
2nd=x+1, 3rd x+2 ... so on
so 6th to 10th term sum = 355
or say
5x+35=355
x=64 1st term

so sum of first 5 terms would be
sn = n/2 ( 2a+(n-1)d)
n=5 , a = 64 d= 1
solve we would get
sn= 330 IMO D
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Re: There is a set of 10 consecutive integers. If the sum of the largest 5  [#permalink]

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New post 26 Dec 2018, 17:50
Jazzmin wrote:
There is a set of 10 consecutive integers. If the sum of the largest 5 integers in the set is 355, what is the sum of the smallest 5 integers?

a. 315
b. 320
c. 325
d. 330
e. 355


Let the no. be x-5, x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4,

Sm of largest 5 integeres =5x+(1+2+3+4)=5x+10=355--> 5x=355-10=345

Sum of smallest 5 integers= 5x-(1+2+3+4+5)=5x-15=345-15=330.

IMO, Option D.
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Re: There is a set of 10 consecutive integers. If the sum of the largest 5 &nbs [#permalink] 26 Dec 2018, 17:50
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