Series Summation Problem

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sanalnnair: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Wed Aug 04, 2010 11:20 am

by sanalnnair » Tue Sep 14, 2010 10:21 am

Hi, Can anyone please help me with this problem??

If each term in the sum a1 + a2 + ......+ an is either 7 or 77 and the sum equals 350, which of
the following could be equal to n??

1) 38

2) 39

3) 40

4) 41

5) 42

Source Gmat Prep

Don't know the answer.

Please help with this problem with the steps. I am confused, how to crack this question.

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Source: Beat The GMAT — Problem Solving | Tue Sep 14, 2010 10:21 am

diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Tue Sep 14, 2010 10:47 am

sanalnnair wrote:Hi, Can anyone please help me with this problem??

If each term in the sum a1 + a2 + ......+ an is either 7 or 77 and the sum equals 350, which of
the following could be equal to n??

1) 38

2) 39

3) 40

4) 41

5) 42

Source Gmat Prep

Don't know the answer.

Please help with this problem with the steps. I am confused, how to crack this question.

because a1+a2+...+an=350 and because a1 or a2 or... an must be 7 or 77
divide 7 from a1+a2..+an=350/7 =50
thus either one a from a1,a2.., an=11 (because you devide 7 from a1+a2+..+an in which there's a number 77 or some )
supposed an=11 thus a1+a2+...+a(11-1)+11=50 so a1+..+a(10)=39
supposed an=11 and a10=11 thus a1+12+..+a9+11+11=50 we will see it couldnt be possible because the smallest number in the answer choice is 38
thus we take A is the answer 2

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Sep 14, 2010 10:48 am

sanalnnair wrote:Hi, Can anyone please help me with this problem??

If each term in the sum a1 + a2 + ......+ an is either 7 or 77 and the sum equals 350, which of
the following could be equal to n??

1) 38

2) 39

3) 40

4) 41

5) 42

Source Gmat Prep

Don't know the answer.

Please help with this problem with the steps. I am confused, how to crack this question.

n = number of terms.
350/7 = 50.
Since the answer choices are less than 50, we can't use all 7's.
If 1 term = 77, 350-77 = 273 remaining.
273/7 = 39. This works.
So we have 1 term of 77, and 39 terms of 7.
n = 1+39 = 40.

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brijesh: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Mon Apr 26, 2010 2:51 amFollowed by: 1 member; Thanked: 6 times

by brijesh » Tue Sep 14, 2010 11:07 am

sanalnnair wrote:Hi, Can anyone please help me with this problem??

If each term in the sum a1 + a2 + ......+ an is either 7 or 77 and the sum equals 350, which of
the following could be equal to n??

1) 38

2) 39

3) 40

4) 41

5) 42

(1+11+1........)=50
lets one set of 11 and 1 = 12 remain= 38 (consider 38 1s) so the total nos= 11s (1) and 1s(39) --total no=40

consider two sets of 11 and 1=24, remain=36 (consider 36 1s) so the total nos= 1s (38) and 11s (2) --total no=40

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