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# If a and b are positive itegers, what is the value of a + b?

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If a and b are positive itegers, what is the value of a + b? [#permalink]

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02 Jul 2012, 03:47
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If a and b are positive integers, what is the value of a + b?

(1) $$\frac{a}{b} = \frac{5}{8}$$
(2) The greatest common divisor of a and b is 1.
[Reveal] Spoiler: OA

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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]

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02 Jul 2012, 04:01
Stiv wrote:
If a and b are positive integers, what is the value of a + b?

1) $$\frac{a}{b} = \frac{5}{8}$$
2) The greatest common divisor of a and b is 1.

Hi,

Using (1),
a/b=5/8
or a=5k & b=8k
thus, a+b = 5k+8k = 13k
k is any integer, Insufficient.

Using (2),
GCD of a & b is 1, of a & b are co-prime. (a,b) = (7, 15) (5, 8) (45, 77). Insufficient,

Combining (1) & (2),
(a,b) = (5, 8), thus, a+b = 13. Sufficient.

Regards,

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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]

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02 Jul 2012, 06:13
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Expert's post
If a and b are positive integers, what is the value of a + b?

(1) $$\frac{a}{b} = \frac{5}{8}$$ --> $$a$$ and $$b$$ could be: (5, 8), (10, 16), (15, 24), ... Not sufficient.

(2) The greatest common divisor of a and b is 1. Clearly insufficient: $$a$$ and $$b$$ could be any co-prime numbers.

(1)+(2) Since from (2) $$a$$ and $$b$$ do not share any common factor but 1, then from (1) $$a=5$$ and $$b=8$$ --> $$a+b=13$$. Sufficient.

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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]

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14 Jan 2015, 22:49
HI All,

This DS question involves a handful of simple math "rules" and can be solved by TESTing VALUES.

We're told that A and B are positive integers. We're asked for the value of A+B

Fact 1: A/B = 5/8

This gives us the ratio of the two integers, but not the integers themselves. It also means that A is a multiple of 5 and B is the equivalent multiple of 8.

IF....
A = 5
B = 8
Then the answer to the question is 13

IF....
A = 10
B = 16
Then the answer to the question is 26
Fact 1 is INSUFFICIENT

Fact 2: The greatest common divisor of A and B is 1

IF....
A = 1
B = 2
Then the answer to the question is 3

A = 5
B = 8
Then the answer to the question is 13
Fact 2 is INSUFFICIENT

Combined, we know
A/B = 5/8; A is a multiple of 5 and B is the equivalent multiple of 8
The greatest common factor of A and B is 1

IF....
A = 5
B = 8
Then the answer to the question is 13

Since A and B are multiples of 5 and 8, respectively, we can stop working. If we take ANY multiple of the two (then those resulting numbers will have a GCF that is GREATER than 1

For Example....
A = 10
B = 16
These numbers have a CGF of 2. This does not match the "restriction" from Fact 2, so it's NOT a useable TEST. None of the possibilities beyond 5 and 8 will "fit" these restrictions, so the answer to the question MUST be 5+8 = 13
Combined, SUFFICIENT.

[Reveal] Spoiler:
C

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If a and b are positive integers, what is the value of a + b? [#permalink]

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09 Jun 2015, 03:56
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So was the answer C or E? My reasoning for C is:

Rearranging the first statement gives us A = 5B/8.

Given both A and B are integers, and that 5 is not divisible by 8, then B must be a multiple of 8.

Also, since B=0 would not be a positive integer value, then B must equal 8 (and so A=5), or 16 (which is 8*2, meaning A = 5*2 = 10), or 24 (which is 8*3, A= 5*3 = 15), or 32 (a = 5*4 = 20) etc.

Note that in every case A and B have the multiple of 8 in common (e.g. if B = 16, which is 8*2, then A = 5*[8*2]/8, which means both A and B will have 2 as a factor). Since statement 2 tells us that they only have 1 as a common factor, B must equal 8 and A must equal 5 (5*[8*1]/8). Answer = C.

I'd appreciate further comments and explanation on this question.

Last edited by ElCorazon on 09 Jun 2015, 04:14, edited 1 time in total.

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Re: If a and b are positive integers, what is the value of a + b [#permalink]

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09 Jun 2015, 04:13
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ElCorazon wrote:
So was the answer C or E? I'd appreciate further explanation if it's C!

Hello ElCorazon

1) From this statement we can infer that 8a = 5b
so more than two variants are possible:
a =5 and b = 8
or a = 50 and b = 80 and so on
Insufficient

2) GCF (a, b) = 1
Insufficient because we know only that a and b is primes or both or one of them equal to 1

1+2) a and b can only be 5 and 8 because all other variant will share some common factor other than 1
for example GCF(50, 80) = 10

Sufficient
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Re: If a and b are positive integers, what is the value of a + b [#permalink]

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09 Jun 2015, 04:16
Thank you - I edited my post before I saw your update - glad to see I was on the right track!

Harley1980 wrote:
ElCorazon wrote:
So was the answer C or E? I'd appreciate further explanation if it's C!

Hello ElCorazon

1) From this statement we can infer that 8a = 5b
so more than two variants are possible:
a =5 and b = 8
or a = 50 and b = 80 and so on
Insufficient

2) GCF (a, b) = 1
Insufficient because we know only that a and b is primes or both or one of them equal to 1

1+2) a and b can only be 5 and 8 because all other variant will share some common factor other than 1
for example GCF(50, 80) = 10

Sufficient

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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]

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16 Mar 2016, 10:03
Here C is sufficient as for any other value of a and b instead of 5 and 8 the GCD will change
hence C
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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]

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18 Oct 2017, 02:50
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Re: If a and b are positive itegers, what is the value of a + b?   [#permalink] 18 Oct 2017, 02:50
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