a and b are integers such that a/b=3.45. If R is the remaind

Question

a and b are integers such that a/b=3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

A. 3
B. 9
C. 36
D. 81
E. 144

Bunuel · Accepted Answer

3.45=\frac{69}{20} , which means that the ratio  \frac{a}{b}=\frac{69}{20} .  a  will be the multiple of  69  ( a=69k ) and  b  will be the multiple of  20  ( b=20k ). For ANY such  a  and  b , the remainder will be multiple of  9  -->  a=qb+r  -->  69k=3*20k+9k .

Only answer choice which is  not  the multiple of 9 is A (3).

Answer: A (3).

fluke · Answer

\frac{Dividend}{Divisor}=Quotient+\frac{Remainder}{Divisor}

\frac{a}{b}=Quotient+\frac{R}{b} --------------------1

3.45 can be written as:
 3+0.45=3+\frac{45}{100}=3+\frac{9}{20}  -----------------2

Correlate 1 and 2:
 Quotient=3 
 \frac{R}{b}=\frac{9}{20}

20R=9b  -----------------3

Expression 3 can only be true if "b" is a multiple of 20 AND "R" is a multiple of 9.

Out of all the options given, only "3" is NOT a multiple of 9.

Ans: "A"

bangalorian2000 · Answer

3.45 = 3(9/20)

Now R can be a 9 or multiple of 9.
A is the figure less than 9 so answer is A

skovinsky · Answer

Hi! This question is a great test of the concept of remainders.

Since a/b = 3.45, we can say that a/b = 345/100. Since a and b must be integers, the smallest possible values will be:

345/100 = 69/20

Rewriting 69/20 with a quotient and a remainder we get 3rem9.

Now we don't know the exact values of a and b, but since we can reduce a/b to 3rem9, we know that the remainder must be a multiple of 9 (and could be any multiple of 9).

B, C, D and E are all multiples of 9: choose (A).

For practice on this concept, there's a 12th edition O.G. question that's very similar - unfortunately, I don't have my copy at home, so I can't cite the exact question number.

martie11 · Answer

Hello...

To build on skovinsky's post, something to remember when you see a remainder question:

\frac{a}{b}=c+\frac{R}{b}

Since  \frac{a}{b}=3.14 ...
 3.14=3+\frac{R}{b} 
Simplify...
 0.14=\frac{R}{b} 
Simplify again...
 \frac{R}{b}=\frac{9}{20}

The last statement tells us that the remainder, R, is a multiple of 9 and the divisor, b, is a multiple of 20. As per answer choices, only A is  not  a multiple of 3.

Hence A.

HTHs.

vraptor · Answer

b X 0.45 = R

=> (R/0.45) should be an integer

A. 3 --> Not an integer 
B. 9 --> Integer
C. 36 --> Integer
D. 81 --> Integer
E. 144 --> Integer

Raptor

enigma123 · Answer

a and b are integers such that a/b=3.45. If R is the remainder of a/b which of the following could NOT be equal to R?

A. 3
B. 9
C. 36
D. 81
E. 144

Ans: a/b=3.45

So considering decimal part: 0.45 = 45/100 where 45 is Remainder and 100 is divisor.

So, R/b=45/100 => 9/20 [I am fine until here]

How can I solve this question after here? Can someone please help? :cry:

BTW the correct answer is (A)

BTW the correct answer is (A)

toughmat · Answer

R/b=45/100 => 9/20 
therefore we have 20R = 9b
For the above to be true R must have a factor 9 as 20 doesnot have a factor 9
Now analyze the answer choices
All options except A have 9 as a factor hence R cannot be equal to A
HTH

shm0401 · Answer

@toughmat,
I could not follow the course of the solution.
Why do we have to take R/b?
What does it denote?

enigma123 · Answer

Because in the question stem it says a/b= 3.45 where a=Dividend and b=divisor. And when we have a remainder with a decimal as we have in this question (0.45) we can re-write this as 45/100 where 45 is the remainder. What we have done is put r=45. Does that make sense? If not then please let me know and I will elaborate.

pkmme · Answer

With a simple example - 
5/2 = 2.5 = 2 + .5 
=> 5 = 2.2 + 2*0.5.

Put the same thing here,
a = 3b + 0.45b

R = 0.45b, check from the options that which one is not divisible by .45. Only A.

Spidy001 · Answer

remainder = 9b/20

and b has to be an integer.

comparing 9b/20 with answer choices , we know Answer A gives non integer value for b.

Hence the answer is A.

bholakc · Answer

I agree with A.
Remainder = 0.45
 = 45/100
 = 9/20

Given, a/b = 3 + 9/29
Remainder(R) = 9b/20

and b has to be an integer.
comparing 9b/20 with answer choices , we know Answer A gives non integer value for b.

Hence the answer is A.

stonecold · Answer

remainder => .45 * B => B is and integer => B=remainder *20/9
hence remainder must be a multiple of 9 => A is not the number 
hence A

ScottTargetTestPrep · Answer

We can create the equation:

a/b = 3 + 45/100

a/b = 3 + 9/20

We see that the remainder is a multiple of 9, so 3 cannot be R.

Answer: A

shishir99776655 · Answer

a/b=3 and 
r/b=0.45=9/20
So remainder is multople of 9 
Option A is not multiple of 9

bumpbot · Answer

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a and b are integers such that a/b=3.45. If R is the remaind

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a and b are integers such that a/b=3.45. If R is the remaind

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