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kaustubh_b: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon Oct 26, 2009 10:55 pm; Thanked: 1 times; GMAT Score:670

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by kaustubh_b » Sat Feb 13, 2010 6:53 am

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

(A)38
(B)39
(C)40
(D)41
(E)42

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Sat Feb 13, 2010 6:53 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Sat Feb 13, 2010 7:12 am

kaustubh_b wrote:This one is from GMAT Prep.
If each term of the series a1 + a2 + ... + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

(A)38
(B)39
(C)40
(D)41
(E)42

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.

If each term of the series a1 + a2 + ... + an is either 7 or 77
If each term of the series a1/7 + a2 /7+ ... + an/7 is either 1 or 11

a1/7 + a2 /7+ ... + an/7 =50

Now if one of the terms is 11 and all others 1s ; no of terms = 39 (1's) + 1 = 40
if two of the terms are 11 and all others 1s ; no of terms = 28 (1's) + 2 = 30
if Three of the terms are 11 and all others 1s ; no of terms = 17 (1's) + 3 = 20
if four of the terms are 11 and all others 1s ; no of terms = 6 (1's) + 4 = 10

These are the only possibilities 40 is given in the choices - hence C

Always borrow money from a pessimist, he doesn't expect to be paid back.

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vscid: Master | Next Rank: 500 Posts; Posts: 212; Joined: Sat Dec 01, 2007 4:19 pm; Thanked: 5 times

by vscid » Sat Feb 13, 2010 10:12 am

This is how I did it, 42 secs.

7x + 77y = 350
x+ y = n

n can have more than 1 values, but in order to maximize n, x has to be maximized.
This is possible when y = 1. So, when y = 1, x = 39.
Hence C.

The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sat Feb 13, 2010 5:15 pm

kaustubh_b wrote:This one is from GMAT Prep.
If each term of the series a1 + a2 + ... + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

(A)38
(B)39
(C)40
(D)41
(E)42

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.

15 second solution: if each term ends in 7, and the sum of the terms ends in 0, then the number of terms MUST be a multiple of 10... choose (C)!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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vscid: Master | Next Rank: 500 Posts; Posts: 212; Joined: Sat Dec 01, 2007 4:19 pm; Thanked: 5 times

by vscid » Sat Feb 13, 2010 5:35 pm

Stuart Kovinsky wrote:
kaustubh_b wrote:This one is from GMAT Prep.
If each term of the series a1 + a2 + ... + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

(A)38
(B)39
(C)40
(D)41
(E)42

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.
15 second solution: if each term ends in 7, and the sum of the terms ends in 0, then the number of terms MUST be a multiple of 10... choose (C)!

Damn ! missed it!