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Intern  Joined: 27 Sep 2010
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What will be the value of a/b ? Given that a and b are  [#permalink]

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10 00:00

Difficulty:   85% (hard)

Question Stats: 47% (01:59) correct 53% (01:48) wrong based on 119 sessions

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What will be the value of a/b ? Given that a and b are positive integers

(1) a^2 – b^2 = 169
(2) a – b = 1

Originally posted by MichelleSavina on 23 Jan 2011, 11:24.
Last edited by MichelleSavina on 23 Jan 2011, 11:39, edited 1 time in total.
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Re: What will be the value of a/b ?  [#permalink]

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MichelleSavina wrote:
Q) What will be the value of a/b ? Given that a and b are positive integers
(1) a2 – b2 = 169
(2) a – b = 1

What will be the value of a/b ? Given that a and b are positive integers

(1) a^2 – b^2 = 169 --> as given that $$a$$ and $$b$$ are positive integers then $$a>b$$. Next, $$a^2-b^2=(a-b)(a+b)=169=1*169=13*13$$ --> again as $$a$$ and $$b$$ are positive integers and $$a>b$$ then $$a-b=1$$ and $$a+b=169$$ --> $$a=85$$ and $$b=84$$ --> $$\frac{a}{b}=\frac{85}{84}$$. Sufficient.

(2) a – b = 1. Clearly insufficient.

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Re: What will be the value of a/b ? Given that a and b are  [#permalink]

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why is it a given that A>B? If the only requirement is that A and B are integers, can't A < B or A = B as well?
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What will be the value of a/b ? Given that a and b are  [#permalink]

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Hi cg0588,

In DS questions, every little piece of information matters, so you have to pay careful attention and take the necessary notes so that you don't miss anything.

Here, the prompt tells us that A and B are POSITIVE INTEGERS, so negatives, 0s and fractions are not possible.

Fact 1 tells us that A^2 - B^2 = 169

Since we're restricted to POSITIVE INTEGERS and A^2 - B^2 = 169, we know that A MUST be bigger than B, thus A > B.

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Re: What will be the value of a/b ? Given that a and b are  [#permalink]

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Ans A

A2-B2 can be written as (A-B)*(A+B)

Stat 1: A2-B2=169 =13*13 or 1*169

Comparing 13*13 with (A-B)*(A+B) we cannot write it in this form using integers
Comparing 1*169 with (A-B)*(A+B) we can write it as (85-84)*(85+84) and this is the only comb => A=85 and B=84 => A/B = 85/84

Stat 2: A-B =1
A can be 3 and B 2...or A=5,B=4...many combinations....so no unique A/B is possible

So Stat 1 alone is Sufficient
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Re: What will be the value of a/b ? Given that a and b are  [#permalink]

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MichelleSavina wrote:
What will be the value of a/b ? Given that a and b are positive integers

(1) a^2 – b^2 = 169
(2) a – b = 1

Given information= a and b are positive integers

(1) a^2 – b^2 = 169

169 has 3 factors 1, 13, 169

(a+b) (a-b)= 13 X 13

Since 169 is +ve number and a and b both are positive (a-b) will be +ve, which means a>b

if a>b and both a and b are positive, then (a+b) and (a-b) both will have different values and those values can be 169 and 1 respectively

a+b= 169
a-b= 1

We can find the value of both a and b and a/b

Statement 1 is sufficient

2) a – b = 1
a and b can have multiple values (3-2 or 5-4 or 9-8 and so on)
Not sufficient

A is the answer
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Re: What will be the value of a/b ? Given that a and b are  [#permalink]

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_________________ Re: What will be the value of a/b ? Given that a and b are   [#permalink] 27 Mar 2019, 08:21
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