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## please explain gmat prep question

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 3 member replies
yvonne12 Master | Next Rank: 500 Posts
Joined
07 Feb 2007
Posted:
144 messages

#### please explain gmat prep question

Sun Apr 01, 2007 3:37 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
if each term in the sum a1, a2 .....an is either 7 or 77 and the sum equals 350 which of the following could equal to n?

ans 40

a)38
b)39
c)40
d)41
e)42

please explain how I can solve problem like these

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800GMAT Master | Next Rank: 500 Posts
Joined
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Sun Apr 01, 2007 4:04 pm
Here is how I approached the problem:

7a + 77b = 350
7(a+11b) = 350
a+11b = 50
here I substituted b=1 and got a=39

Since n = a+b
therefore, n = 1+39 =40, which is one of the answer choices.

If 40 was not one of the answer choices i would have put other values for b to match one of the answer choices.

yvonne12 Master | Next Rank: 500 Posts
Joined
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Posted:
144 messages
Mon Apr 02, 2007 10:46 am

### Top Member

Roland2rule Master | Next Rank: 500 Posts
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Fri Sep 29, 2017 2:41 pm
let say x is the number of times 7 represent.
7x + 7 (11)(n-x) = 350
divide through by 7
x + 11(n-x) = 50
x=39, then trying option C which is 40 (i.e n=40)
39+11(1)=50

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Fri Sep 29, 2017 4:09 pm
Quote:
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?

A)37
B)39
C)40
D)41
E)42

Notice that 77 does not divide into 350 many times.
In fact, there can be, at most, four 77's in the sum
So, there are only 5 cases to consider (zero 77's, one 77, two 77's, three 77's and four 77's)
It shouldn't take long to check the cases.

case 1: zero 77's in the sum
If every term is 7, the total number of terms is 50.
50 is not one of the answer choices, so move on.

case 2: one 77 in the sum
350 - 77 = 273
273/7 = 39
So, there could be thirty-nine 7's and one 77 in the sum, for a total of 40 terms.

This matches one of the answer choices, so the correct answer is C

Cheers,
Brent

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
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Fri Sep 29, 2017 4:09 pm
Quote:
If each term in sum a1+a2+ ... +an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

A)37
B)39
C)40
D)41
E)42
Another possible approach it to look for a pattern:

Since both 7 and 77 have 7 as their units digit, we know that if we take any two terms, their sum will have a units digit of 4 (e.g., 7 + 7 = 14, 7 + 77 = 84, 77 + 77 = 154)

Similarly, if we take any three terms, their sum will have a units digit of 1. (e.g., 7 + 7 + 7 = 21, 7 + 7 + 77 = 91, etc.)

Now let's look for a pattern.

The sum of any 1 term will have units digit 7
The sum of any 2 terms will have units digit 4
The sum of any 3 terms will have units digit 1
The sum of any 4 terms will have units digit 8
The sum of any 5 terms will have units digit 5
The sum of any 6 terms will have units digit 2
The sum of any 7 terms will have units digit 9
The sum of any 8 terms will have units digit 6
The sum of any 9 terms will have units digit 3
The sum of any 10 terms will have units digit 0
The sum of any 11 terms will have units digit 7 (at this point, the pattern repeats)

From this, we can conclude that the sum of any 20 terms will have units digit 0
And the sum of any 30 terms will have units digit 0, and so on.

We are told the sum of the terms is 350 (units digit 0), so the number of terms must be 10 or 20 or 30 or . . .

Since C is a multiple of 10, this must be the correct answer.

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
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