gmat prep question

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san2009: Master | Next Rank: 500 Posts; Posts: 171; Joined: Fri Apr 16, 2010 1:02 am; Thanked: 1 times

by san2009 » Wed Jun 16, 2010 7:54 am

Please provide a conceptual/methodological approach only

If each term in the sum a1 + a2 + a3...+ an is either 7 or 77 and the sum equals 350, which of the following could be n?

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

OA is C

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Source: Beat The GMAT — Problem Solving | Wed Jun 16, 2010 7:54 am

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Jun 16, 2010 8:02 am

There are n terms, and each term is either 7 or 77. This means if we factor out 7 from the expression, we have either 1 or 11 in parenthesis.

We can therefore reduce the problem to:

Each term in the sum b1 + b2 + b3+...+bn is either 1 or 11, and the sum equals 50. What could n be?

Let's start by assuming there are no 11's. This means there must be 50 1's => n= 51 (Not in the choice)
Continuing on this trend:

1 eleven and 39 1's n = 40 (In our choice! Pick it

)

Pick C

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Wed Jun 16, 2010 8:20 am

7a+77b=350

a+11b=50

Plug in the options in the above equation,we will get a =39 and b=1

n=40

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Wed Jun 16, 2010 8:20 am

If each term in the sum a1 + a2 + a3...+ an is either 7 or 77 and the sum equals 350, which of the following could be n?

A) 38
B) 39
C) 40
D) 41
E) 42
350 if you divide by 7 you will get 50 so you can havefifties 7 but we need to include 77 also
now let us include one 77
so we can have 350-77=273/7= 39 7's
so n could be 40

now let us take 2 77's now number of 7 will be (350-(77*2))/7=28 7's so n will be 30 in that case
so from given option we can conclude answer will be 40
cheers

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Jun 16, 2010 8:31 am

san2009 wrote:Please provide a conceptual/methodological approach only

If each term in the sum a1 + a2 + a3...+ an is either 7 or 77 and the sum equals 350, which of the following could be n?

7+77+77+...
Let number of 7's be x and 77's be y

7x+77y = 350
x+11y= 50, both x and y are positive integers.
y = (50-x)/11 should be an integer. So 50-x should be multiple of 11.

50-x = 11 -> x =39, y = 1
50-x =22 -> x=28, y=2
50-x = 33 -> x = 17, y=3,
50-x = 44 -> x = 6, y=4

we need x+y so answers are, 40,30,20,10

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