If a and b are positive integers so that the remainder, when dividing

Question

If a and b are positive integers so that the remainder, when dividing a by b, is 4, which of the following could be the value of  \frac{a}{b} ?

A.  \frac{3}{4}

B.  \frac{1}{3}

C.  \frac{5}{8}

D.  \frac{5}{7}

E.  \frac{7}{8}

This is a  PS Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Critical Reasoning Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

Purnank · Answer

IMO B

Using option B, multiply by 4 on both numerator and denominator we will get the 4/12 from there we can get the remainder 4.

Correct me if i am wrong here.

satvikd22 · Answer

Can we get the solution here. How do we approach such problems ?

BrushMyQuant · Answer

Remainder of a by b is 4 and we need to find the value of  \frac{a}{b}

Ideally we would have wanted option choices for  \frac{a}{b}  like  \frac{7}{3}  or  \frac{4}{7}  which will directly give us the remainder of 4, but that is not the case.

Note that in all the option choices we have numerator smaller than the denominator.
So, only way to get values of  \frac{a}{b}  is to start multiplying the numerator and the denominator till the time numerator becomes 4

Now, that is only possible is option 1 as all other numbers are odd numbers bigger than 1

So,  \frac{1}{3}  *  \frac{4}{4}  =  \frac{4}{12}  =  \frac{a}{b} 
Making, a as 4 and b as 12 and the remainder of a by b as 4.

So,  Answer will be B 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

Sujithz001 · Answer

Bunuel  /  KarishmaB  can you please provide the explanation here?

Thanks!

KarishmaB · Answer

All the options are less than 1 so the value of a/b is less than 1. This means a < b and hence the remainder when we divide a by b will be a. Since this remainder is given to be 4, we know that a = 4. 
The only option in which a can be 4 is 1/3. If a = 4, b = 12 - works.
 
For no other option can a be 4 while getting an integer value for b.

Answer (B)

If a and b are positive integers so that the remainder, when dividing

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

If a and b are positive integers so that the remainder, when dividing

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