For positive integers a, b, and c, b is 120% greater than a, and c is

Question

For positive integers a, b, and c, b is 120% greater than a, and c is 25% less than the sum of a and b. Which of the following could be the value of |a – c| ?

(A) 6

(B) 7

(C) 8

(D) 9

(E) 10

CrackverbalGMAT · Accepted Answer

Since a, b and c are integers, |a - c| will also be an integer

b = 120% greater than a = 2.2a

c = 75% (a + b) = 0.75 (a + 2.2a) = 0.75 * 3.2a = 2.4a

|a - c| = |a - 2.4a| = |-1.4a| = 1.4a

a has to be multiples of 5, so that the difference is an integer.

a = 5 gives 1.4a = 7. Higher multiples of a will give values of multiples of 7 which are not among the options

Option B

Arun Kumar

ScottTargetTestPrep · Answer

Solution:

Since b is 120% greater than a, b = 2.2a. Then, the sum of a and b is a + b = a + 2.2a = 3.2a. Since c is 25% less than the sum of a and b, c = 3/4 * 3.2a = 2.4a. Thus:

|a - c|

|a - 2.4a|

|-1.4a|

|1.4a|

|14a/10| = |7a/5|

7/5 * |a|

Notice that since a and c are integers, |a - c| is also an integer. No matter what the value of a is, the expression 7/5 * |a| is a multiple of 7. We see that the only multiple of 7 among the answer choices is 7.
 Answer: B

Archit3110 · Answer

given that a,b,c are all integers
let a be integer a so b which is 120% greater than a is 2.2a
and c = .75*(a+2.2a) ; 2.4a
value of la-cl = la-2.4al ; 1.4a
out of given answer values the value of integer of a stands at 7 only i.e. a = 5 , b= 11 and c = 12
sufficient
option B

UserMaple5 · Answer

My solution:

Let a = 100
Then b = 100 + 120% of 100 = 220
So a + b = 320

Since C is 25% less than a + b, 
c = 320 - 25% of 320 = 240

So |a - c| = |100 - 240| = 140.

Since a, b, c are positive integers, looking at answer choices, the only one that's a multiple of 7 is 7. Hence Answer is B

BrushMyQuant · Answer

b is 120% greater than a

=> b = a + 120% of a = a +  \frac{120}{100}  * a = a + 1.2a = 2.2a

c is 25% less than the sum of a and b

=> c = 75% of sum of a and b = 75% * (a+b) = 0.75a + 0.75b = 0.75a + 0.75*2.2a = 0.75a + 1.65a = 2.4a

|a – c| = | a - 2.4a| = |-1.4a| = 1.4a (as a is positive integer) =  \frac{14}{10}  * a =  \frac{7}{5}  * a

Since a is an integer so  \frac{7}{5}  * a will be a multiple of 7 
=>  \frac{7}{5}  * a = 7 (when a = 5)

So,  Answer will be B 
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

Usernamevisible · Answer

Easier solution is take a as 5, get b as 11 and c as 12
Difference of 7 thus b

For positive integers a, b, and c, b is 120% greater than a, and c is

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For positive integers a, b, and c, b is 120% greater than a, and c is

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