If a, b, and c are consecutive positive integers where a

Question

If a, b, and c are consecutive positive integers where a < b < c, and c - a = 16/b, then a + b + c =

A. 30
B. 24
C. 18
D. 12
E. 6

PS20355

BrentGMATPrepNow · Accepted Answer

If a, b, and c are  consecutive positive integers  where a < b < c, then we know that:
a + 1 = b 
And, more importantly, a + 2 = c 
If a + 2 = c, then  c - a = 2

GIVEN: c - a = 16/b 
Substitute to get:  2  = 16/b
Solve: b =  8

So, a, b and c equal 7,  8 , and 9 respectively
This means a + b + c = 7 +  8 + 9 = 24

Answer: B

Cheers,
Brent

Archit3110 · Answer

c - a = 16/b
x+2-x= 16/x+1
x= 7
so a+b+c ; 7+8+9 ; 24
OPTION B

NitishJain · Answer

B. a,b, c are consecutive integers and a b = 8 ==> a= 7; b= 8; c =9 a+b+c = 7+8+9 = 24

CrackverbalGMAT · Answer

a, b, and c are consecutive positive integers where a < b < c

So,b = a + 1

c = a + 2

a + b + c = a + a+1 + a+2

=3a + 3

=3(a+1)

=3b...(1) [As a + 1 =b]

c - a = 16/b

=>a+2 - a =16/b

=>b=8

So, in equation 1,

a +b +c = 3b =3 * 8 =24
(option b)
D.S
GMAT SME

BrushMyQuant · Answer

Given that a, b, and c are consecutive positive integers where a < b < c, and c - a = 16/b and we need to find the value of a + b + c

As a, b and c are consecutive positive integers
=> b = a + 1
=> c = b + 1 = a + 2

=> c - a = a + 2 - a = 2 = \(\frac{16}{b}\) (given)
=> b = \(\frac{16}{2}\) = 8

=> a = b - 1 = 7
=> c = b + 1 = 9

=> a + b + c = 7 + 8 + 9 = 24

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Sequence problems

DanTheGMATMan · Answer

Easy if you realize that c-a=2:

https://www.youtube.com/watch?v=d_K1_VcR04I

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a, b, and c are consecutive positive integers where a < b < c, and

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions