When positive integer a is divided by positive integer b, yielding quo

Question

When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125. Which of the following must be true?

A. r=1
B. q>r
C. b=8
D. 8r=b
E. 8b=r

chetan2u · Accepted Answer

Given is a=5.125b=(5+0.125)b...
Here 0.125b is the remainder...
So 0.125b=r...
0.125 is nothing but  \frac{1}{8} ......
So  \frac{b}{8}=r........b=8r ...
D

warriorguy · Answer

a/b = Q + r/b

r/b = 0.125 = 1/8

b=8r

D

sakeofall · Answer

What if we pick numbers 82 for  a  and 16 for  b ? Then D isn't true (r = 0.125, b = 16), but the intent of the passage is preserved, right?

Funsho84 · Answer

a/b = q + r
a/b = 5 + .125

r/b = 125/1000

r/b = 1/8

8r=b

Mo2men · Answer

\frac{82}{16} = 5 + \frac{2}{16}

r/b = 2/16 = 1/8 = 0.125.........D holds true in that case too. b = 8r (16 = 8 *2)

ScottTargetTestPrep · Answer

We can create the equations:

a/b = q + r/b

and

a/b = 5 + 0.125

a/b = 5 + 125/1000

a/b = 5 + 1/8

Thus,

r/b = 1/8

8r = b

Answer: D

breatheanddoit · Answer

how did you come on this conclusion?

ScottTargetTestPrep · Answer

Since a/b = Q + r/b and a/b = 5 + 1/8:

We can say that r/b= 1/8

Fdambro294 · Answer

Rule to remember with respect to remainders and a terminating decimal. It will always be true that:

(Decimal Portion of Quotient) * (Divisor) = Integer Remainder

a/b = 5.125

Decimal Version of the Remainder = .125

Divisor = b

We are told that the integer remainder = r

(.125) (b) = r

Fraction Conversion to memorize: 1/8 = .125

(b) / (8) = r

—-multiply both sides by *8—-

b = 8r

Posted from my mobile device

ManishaPrepMinds · Answer

a ÷ b = 5.125 where a, b are positive integers

we know:  a = bq + r where 0 ≤ r < b 
Divide both sides of the above equation by b
a/b = q + r/b 
Since a / b = 5.125
When we divide integers and get a decimal result, we can extract:
Quotient (q): Integer part = 5
Decimal part( r/b): 0.125 represents the remainder over the divisor

r/b = 0.125 = 1/8
-> 8r= b

Answer: D

hayleighshields · Answer

Can someone explain why it is not B?

ManishaPrepMinds · Answer

We are given:
a ÷ b = 5.125 → a / b = q + r / b

From this:
q = 5 (Integer part of 5.125)
r / b = 0.125 = 1/8 → r = b / 8

So, as b increases, r also increases

But q = 5 is fixed.

Therefore, q > r is not always true.

Example: 
If b = 16 → r = 2 
→ q = 5 → q > r  TRUE 
If b = 48 → r = 6
→ q = 5 → q < r  FALSE

So option B (q > r) is not always true.

When positive integer a is divided by positive integer b, yielding quo

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 positive integer a is divided by positive integer b, yielding quo

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