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Sequence Question

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Sequence Question

by exhilaration » Fri May 29, 2009 12:15 pm
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?

38

39

40

41

42

C

Along the same lines....a DS question:

The sum of positive integers x and y is 77. What is the value of xy?

(1) X = y+1

(2) x and y have the same tens digit

D



Thanks for your help guys
Last edited by exhilaration on Fri May 29, 2009 11:39 pm, edited 1 time in total.
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Re: Sequence Question

by dtweah » Fri May 29, 2009 3:42 pm
exhilaration wrote:If each term in the sum a1 + a2 +....+an is either 7 or 7 and the sum equals 350, which of the following could be equal to n?

38

39

40

41

42

C

Along the same lines....a DS question:

The sum of positive integers x and y is 77. What is the value of xy?

(1) X = y+1

(2) x and y have the same tens digit

D



Thanks for your help guys
7X +77y=350
x+11y=50
x+y =n
n=50-10y
y=1
n=40

Choose C.

1) solves A trivially.

2. 10a +b
10a +c

70 + 7=77


b+c=7
20a=70
a=7/2

35+ b
35 +c

b and c must be such that they don't affect the 3 in 35 ie 5 +b and 5+c <10 .Possible b and c are 0 7, 1 6, 2 5, 3 4 All violate this condition save the 3rd. b, c is 3, 4 vice versa.

38 +39=77

Choose D.
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by exhilaration » Fri May 29, 2009 4:20 pm
Thanks!

Just wanted to clarify...

7X +77y=350
x+11y=50
x+y =n
n=50-10y
y=1
n=40

How did you calculate that y=1?
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by dtweah » Fri May 29, 2009 5:08 pm
exhilaration wrote:Thanks!

Just wanted to clarify...

7X +77y=350
x+11y=50
x+y =n
n=50-10y
y=1
n=40

How did you calculate that y=1?
Y can only take on 4 values 1 2 3 4. It cannot be 0 and 5. Of the 4 only 1 produces an n among the answer choices. If there were no answer choices, of course then x would come into play to figure it out.
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Re: Sequence Question

by sureshbala » Fri May 29, 2009 10:12 pm
exhilaration wrote: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?

38

39

40

41

42

C

Along the same lines....a DS question:

The sum of positive integers x and y is 77. What is the value of xy?

(1) X = y+1

(2) x and y have the same tens digit

D



Thanks for your help guys
Please make a correction in the first question. It has to be 77 and not 7.

Anyway here are the solutions

This can be answered very quickly in the following manner.

If all of them are 7s, then we need 50 terms.

Now every 11 7s can be replaced with one 77.

So, the number of terms will always be in the form

50 - 11x + x = 50-10x.

So for x = 1, we get number of terms as 40.

2.

Statement I is clearly stating that that x is 39 and y is 38.

Coming to statement 2:

Since x+y = 77 and 77 is odd, definitely one of them must be even and the other must be odd. Also, since the ten's digit is same for both x and y they must be consecutive numbers.

Thus statement 2 is same as statement 1.

Hence sufficient
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Re: Sequence Question

by exhilaration » Sat May 30, 2009 12:02 pm
sureshbala wrote:
exhilaration wrote: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?

38

39

40

41

42

C

Along the same lines....a DS question:

The sum of positive integers x and y is 77. What is the value of xy?

(1) X = y+1

(2) x and y have the same tens digit

D



Thanks for your help guys
Please make a correction in the first question. It has to be 77 and not 7.

Anyway here are the solutions

This can be answered very quickly in the following manner.

If all of them are 7s, then we need 50 terms.

Now every 11 7s can be replaced with one 77.

So, the number of terms will always be in the form

50 - 11x + x = 50-10x.

So for x = 1, we get number of terms as 40.

2.

Statement I is clearly stating that that x is 39 and y is 38.

Coming to statement 2:

Since x+y = 77 and 77 is odd, definitely one of them must be even and the other must be odd. Also, since the ten's digit is same for both x and y they must be consecutive numbers.

Thus statement 2 is same as statement 1.

Hence sufficient
Thanks everyone!
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