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

Question

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

Bunuel · Accepted Answer

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.

Answer: A.

cg0588 · Answer

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?

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

bullseye800 · Answer

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

Divyadisha · Answer

Given information= a and b are positive integers 
Question asked=a/b?

(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

Aannie · Answer

Explanation:
Given that a and b are positive integers. ⇒ a + b and a − b will also be integers

Considering statement 1:
a2 − b2 = 169
⇒ (a − b)(a + b) = 169 = 13 × 13
Now there are 4 possibilities for a + b and a − b: 1, 169 or 13, 13 or −1, −169 or −13, −13.

Case 1:
a + b = 169 and a − b = 1
Solving 2 equations => a = 85 and b = 84

Case 2:
a + b = 13 and a − b = 13
Solving 2 equations ⇒ a = 13 and b = 0
Since a and b are positive integers, so these values can be rejected.

Case 3:
a + b = −1 and a − b = −169
Solving 2 equations ⇒ a = −85 and b = −84
Since a and b are positive integers, so these values can be rejected.

Case 4:
a + b = −13 and a − b = −13
Solving 2 equations ⇒ a = −13 and b = 0
Since a and b are positive integers, so these values can be rejected.

Since we are getting a definite answer from above statement (only Case 1), statement 1 itself is sufficient to provide the answer.

Considering statement 2:
a − b =1
As only known information is that a and b are positive integers , infinite values of a and b are possible for which a − b =1.

Since we are not getting a definite answer from above statement , statement 2 also itself is not sufficient to provide the answer.

Answer: A

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

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GMAT Data Sufficiency (DS) Questions

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

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