When positive integer A is divided by positive integer B

Question

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when A is divided by B?

(A) 13 
(B) 14 
(C) 15 
(D) 16 
(E) 17

kp1811 · Accepted Answer

we know that A,B are +ve integers and when A is divided by B we get 4.35. This 4 is the quotient obtained when A is divided by B. We get 0.35 because A is not prefectly divisible by B and this 0.35 is the remainder which we need to find out in terms of whole numbers

0.35 = 35/100 (shifting the decimal 2 places to make it a whole number)
this 35/100 is the remainder for A/B. On simplifying we get 7 as the remainder if B =20

Now we know quotient is 4 so if B = 20 A will be 4*20 + 7 = 87 (A/B gives 4.35)
If B = 100 then A will be 4*100 + 35 = 435 (A/B gives 4.35)
If B = 60 then A will be 4*60 + 21 = 261 (A/B gives 4.35)

so we can see that remainder in this case will be a multiple of 7. of the given option 14 satisfies this.
hope this helps

BrentGMATPrepNow · Answer

Notice that 0.35 = 35/100

So, we can write: A/B = 4 35/100 = 435/100
So, one possible case is that A = 435 and B = 100
When we divide 435 by 100, the remainder is 35
Unfortunately 35 is NOT one of the answer choices.

Now let's examine some fractions that are EQUIVALENT to 435/100
For example, 435/100 = 87/20 (= 4.35)
In other words, A = 87 and B = 20
In this case, when we divide A by B, the remainder is 7
Unfortunately 7 is NOT one of the answer choices.

Find another fraction EQUIVALENT to 435/100
How about 174/40 (= 4.35)
In other words, A = 174 and B = 40
In this case, when we divide A by B, the remainder is 14
Aha, 14 IS one of the answer choices!!

Answer: B

RELATED VIDEO 
 https://www.youtube.com/watch?v=XCxgIR042tE

kp1811 · Answer

the remainder will be obtained from the decimal part when A is divided by B i.e. 0.35

0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this

PS: for B-14 A=174 and B=40

prasadrg · Answer

Thank you for solving. I am still not clear the concept behind dividing 35/100 to get the reminder.

How do we assume 100 here?

I know it is subtle, and I am not able to catch it. Appreciate your help.

prasadrg · Answer

Thank you very much for the detailed explanation and it makes sense.

Appreciate.

Bunuel · Answer

Similar questions to practice: when-positive-integer-x-is-divided-by-positive-integer-y-106493.html if-s-and-t-are-positive-integers-such-that-s-t-64-12-which-135190.html

ScottTargetTestPrep · Answer

We can create the following equation:

A/B = 4.35

A/B = Q + 35/100

A/B = Q + 7/20

We see that the remainder is a multiple of 7; thus, the remainder could be 14.

Answer: B

adkikani · Answer

ScottTargetTestPrep   GMATPrepNow   niks18   gmatbusters   Bunuel

I did not get the highlighted part. In the question stem, we are only given that dividend and
divisor are positive integers, is it an inherent property that a remainder will always be an integer?

GMATBusters · Answer

adkikani

The remainder is the  integer  "left over" after dividing one integer by another to produce an integer quotient (integer division).

dividend = (integer quotient)*(divisor) + remainder (integer)

The  Remainder is a integer always less than divisor.

In the division of 43 by 5 we have:

43 = 8 × 5 + 3,
so 3 is the remainder.

I did not get the highlighted part. In the question stem, we are only given that dividend and
divisor are positive integers, is it an inherent property that a remainder will always be an integer?

AyushCrackVerbal · Answer

Given:

\frac{A}{B}  = 4.35 = 4 + 0.35

A = 4B + 0.35B

Since A and B are positive integers, 4B is also a positive integer and 0.35B also will be a positive integer.

The remainder is 0.35B. We'll equate 0.35B with the given options to find the possible answer:

0.35B =  \frac{35}{100} B =  \frac{7}{20}  B

Now,

If  \frac{7}{20}  B = 13, B will not be an integer.

If  \frac{7}{20}  B = 14, B will be an integer.

If  \frac{7}{20}  B = 15, B will not be an integer.

If  \frac{7}{20}  B = 16, B will not be an integer.

If  \frac{7}{20}  B = 17, B will not be an integer.

The correct answer is  B

akankshathareja · Answer

A/B = 4.35 = 4 + 0.35
A = 4B + 0.35B
The latter part is our remainder. => r = 0.35B
r/0.35 = B
r*100/35 = B

Now, since B is an Integer, we need to find an option that resolves   into an Integer. Only option C (i.e. r=14) satisfies it.

Answer = C

MathRevolution · Answer

A is divided by positive integer B, the result is 4.35

=>  \frac{A }{ B}  = 4.35

=>  \frac{A }{ B}  =  \frac{435 }{ 100}

So, Let A be 435 and B be 100 giving result as 4.35.

Simplifying,  \frac{435 }{ 100 }

=> 4+  \frac{35 }{ 100}

35/ 100 is a remainder which can be further simplified as  \frac{7 }{ 20} .

So, the remainder has to be multiple of 7.

Option 14 satisfies it.

Answer B

BrushMyQuant · Answer

When positive integer A is divided by positive integer B, the result is 4.35

\frac{A}{B}  = 4.35
=> A = B*4.35 = B *(4 + 0.35)
=> A = B*4 + B*0.35
=> A when divided by B gives 4 as Quotient and 0.35B as remainder

=> B *0.35 is an integer
Remainder = B *  \frac{35}{100}  = B *  \frac{7}{20}  
=  \frac{B}{20}  * 7
=> Remainder is a multiple of 7
Only, option choice possible is 14

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Remainders

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

road740 · Answer

B. Quick solution to this: If \frac{A}{B} = 9.35, then 0.35 * B = remainder. Now try it out: (A) 13 = 0.35*B <=> \frac{13}{0.35} = B <=> B = \frac{13*20}{7} <-- not an integer! (B) 14 = 0.35*B <=> ... <=> B = 40 <-- integer! --> (B) is the correct answer.

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When positive integer A is divided by positive integer B

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