When x is divided by a, the quotient is b and the remainder is c. If a

Question

When x is divided by a, the quotient is b and the remainder is c. If a, b, c and x are different positive integers, what is the smallest possible value of x?

A) 4
B) 5
C) 6
D) 7
E) 8

Archit3110 · Answer

We have
X=a*b+c
Using answer options
Smallest value of X can be 5
5=3*1+2
Option B

Posted from my mobile device

Hoozan · Answer

Concept:  Dividend = Divisor x Quotient + Remainder

Keeping the above in mind we can convert the question into an algebraic equation and say  \frac{x}{b}  = a +  \frac{c}{b}

In other words, x = ab + c

We need to find the least value of X i.e. least value of ab + c. Since a ≠ b ≠ c, we need to take the least consecutive integers i.e. 1,2, and 3.

Let a = 3 ; b = 1 and c = 2

So we get x = 3(1) + 2 = 5

We can check our answer.

\frac{5}{3}  = 1 +  \frac{2}{3}  Or 5 = 3(1) + 2

Correct answer: (B)

BrentGMATPrepNow  could you show your method? How could you arrive at the answer <1 min?

BrentGMATPrepNow · Answer

------ASIDE---------------
There's a nice rule that says, "  If N divided by D equals Q with remainder R, then N = DQ + R  "
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
---------------------------

From the given information, we can write  x = ab + c 
We want to minimize the value of x. 
Also keep in mind that a, b, c and x are  different  positive integers.

So let's test the three smallest positive integers, 1, 2 and 3.

If a = 1, b = 2 and c = 3, then  x = ab + c = (1)(2) + 3 = 5 
If a = 2, b = 1 and c = 3, then  x = ab + c = (2)(1) + 3 = 5     
If a = 1, b = 3 and c = 2, then  x = ab + c = (1)(3) + 2 = 5 
If a = 2, b = 3 and c = 1, then  x = ab + c = (2)(3) + 1 = 7

So, 5 is the smallest possible value of x.

Answer: B

Hoozan · Answer

BrentGMATPrepNow  don't you mean (B) 5 is the correct answer

Posted from my mobile device

BrentGMATPrepNow · Answer

Oops, not sure where 6 came from

All fixed! Kudos for you!!!!

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.

When x is divided by a, the quotient is b and the remainder is c. If a

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

When x is divided by a, the quotient is b and the remainder is c. If a

Prep Toolkit

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