Integer d is the product of the integers a, b, and c and 1

Question

Integer d is the product of the integers a, b, and c and 1 < a < b < c. If the remainder when 233 is divided by d is 79, what is the value of a+c?

A. 7 
B. 9 
C. 13 
D. 14 
E. 18

chetan2u · Answer

d=a*b*c.....
If 233 lives a Remainder 79 when div by d, 233-79 or 154 should be div by d...

154=1*2*7*11..
Now 1<a<b<c and a*b*c=2*7*11, a+c=2+11=13
C

Nikkb · Answer

given d= a*b*c 1 d= 154 so a*b*c = 154 = 2*7*11 => a=2 and c=11 => a+c = 2+11 =13 Answer: C

kaulshanx · Answer

233=dx+79 which is the equation of the remainder. Simplifying the equation becomes - dx=154 and it is given that d=a*b*c so substituting the value of d in above equation we get (abc)*x=154. Now prime factorization of 154 is 2*7*11 and assuming the quotient i.e. x=1 and considering the condition given ie. 1<a<b<c. This states that a=2, b=7 & c=11. So a+c=2+11=13, hence the answer is C.

Sent from my SM-N920G using GMAT Club Forum mobile app

Sent from my SM-N920G using  GMAT Club Forum mobile app

pushpitkc · Answer

233 can be divided by 79 or 158 to give us a remainder of 79

When divided by 158, the difference is 75(3*5^2) but a < b < c
But, when divided by 79, the difference is 154(2*7*11). 
Here 1 < a=2 < b=7 < c=11!

Therefore, a+c = 2+11 =  13(Option C)

ScottTargetTestPrep · Answer

We see that 233 = dq + 79 where q is a positive integer. Simplifying, we have dq = 154. Since 154 = 14 x 11 = 2 x 7 x 11 and d is a product of 3 distinct positive integers greater than 1, we see that q must be 1 and d must be 154, and hence a = 2, b = 7 and c = 11. So a + c = 2 + 11 = 13.

Answer: C

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.

Integer d is the product of the integers a, b, and c and 1 < a < b < c

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