When the integer x is divided by the integer y, the remainder is 60.

Question

When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?

I. 15.15 
II. 18.16 
III. 17.17

(A) I only 
(B) II only 
(C) III only 
(D) I and II only 
(E) I and III only

Bunuel · Accepted Answer

"x is divided by the integer y, the remainder is 60" -->  x=qy+60  --> or  \frac{x}{y}=q+\frac{60}{y} , so basically  \frac{60}{y}  is a decimal portion of  \frac{x}{y} .

For example:  \frac{x}{y}=15.15  means that  \frac{x}{y}=15+0.15=15+\frac{60}{y}

Let's look at the options:

I. If  \frac{x}{y}=15.15  then  \frac{60}{y}=0.15  and  y=400=integer , which is possible;

II. If  \frac{x}{y}=18.16  then  \frac{60}{y}=0.16  and  y=375=integer , which is possible;

III. If  \frac{x}{y}=17.17  then  \frac{60}{y}=0.17  and  y=\frac{6000}{17}
eq{integer} , which is not possible as  y  must be an integer.

Answer: D.

alphabeta1234 · Answer

Bunuel,

I am confused by the terminology of the question. When x is divided by y the remainder 60. is x=yk+60. "y" is the quotient and the question is asking for possible quotients, ie, possible y values.

But in your solution you have x/y=quotient. Very confused.

Narenn · Answer

In x=yk+60, y = divisor and k = quotient.

On dividing both sides of the equation by Y -------->  \frac{x}{y} = \frac{(yk)}{y} + \frac{60}{y}  -------->  \frac{x}{y} = k + \frac{60}{y}

So k = quotient and  \frac{60}{y} is Remainder. -------- Quotient can not be fraction.

So while considering 15.15 we should recognize that 15 must be quotient and 0.15 must be remainder, but the remainder is  \frac{60}{y} ---------> Hence  0.15 = \frac{60}{y}  ------->  Y = \frac{60}{0.15}  -------> Y = 400

Note that we are told that Y is integer so basically we are just looking for whether given expression could give the integer value of Y

Consider second option 18.16 ------> Y = 60/0.16 -------> 6000/16 ------> some integer

In 17.17 ---------> 60/0.17 -------> 6000/17 ------> Not an Integer

Hope that helps

rhallik · Answer

Hello!

Would it be possible to solve the task as follows:

I. We know that the reminder is 15. As 60 is divisible by 15 we can assume that 15.15 could be one solution.
II. We know that the reminder is 16 which is 2*8. As 60 can be divided by 2 we can assume that 18.16 could be one solution.
III. We know that the reminder is 17. As 60 is not divisible by 17 or vice versa, we can assume that 17.17 cannot be one of the solutions.

Also, please explain if my approach has a flaw.

Thank you in advance!

Narenn · Answer

I think, it will not work every time. I will show you how.

Let's change the third option. Lets assume Remainder is 21 and quotient is 5.10

We know that the remainder is 0.10 As 21 is not divisible by 10 or vice versa, we can assume that 5.10 cannot be one of the solutions. Can this be true??
21/0.10 ------> 2100 / 10 ---------> well divisible by 10.

in the division 21/0.10 when you move the decimal sign of denominator to the right by two places, you add two zeros in the numerator to create the fraction 2100/10
When you are awarding two zeros to the numerator (i.e. to 21) remember you are actually giving 2 twos and 2 fives to the numerator. Why is so. That is because One zero can be obtained by multiplying 5 with 2
Now since the denominator (i.e. 10) contains 1 five and 1 two and since you just have given 2 fives and 2 twos, you can surely divide numerator by the denominator.

JeffTargetTestPrep · Answer

Letting Q = the quotient, we can use the expression:

x/y = Q + 60/y

We see that 60/y is the remainder. We can set this to the decimal portion of each value in the Roman numerals and solve for y.

I. 15.15

60/y = 0.15

60 = 0.15y

y = 60/0.15 = 6000/15 = 400

We see that 15.15 could be a value of x/y since we have y as an integer.

II. 18.16

60/y = 0.16

60 = 0.16y

y = 60/0.16 = 6000/16 = 375

We see that 18.16 could be a value of x/y since we have y as an integer.

III. 17.17

60/y = 0.17

60 = 0.17y

y = 60/0.17 = 6000/17 = 352.94

We see that 17.17 could NOT be a value of x/y since we DON’T have y as an integer.

Answer: D

KarishmaB · Answer

First check this video that discusses the decimal representation of remainders: https://youtu.be/A5abKfUBFSc The decimal part gives us the possible remainders and the divisors. I. 15.15 = 15 + 0.15 = 15 + \frac{15}{100}=15 + \frac{3}{20} So the remainder can be any multiple of 3 here and the corresponding divisor will be the same multiple of 20. Hence the remainder can be 60 here since it is a multiple of 3. II. 18.16 = 18 + \frac{16}{100}=18 + \frac{4}{25} So the remainder can be any multiple of 4 here and the corresponding divisor will be the same multiple of 25. Hence the remainder can be 60 here since it is a multiple of 4. III. 17.17 = 17 + \frac{17}{100} Since 60 is not a multiple of 17, the remainder cannot be 60 here. Answer (D)

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=_yqmszWk0kY

When the integer x is divided by the integer y, the remainder is 60 
=> x = y*q + 60, where q is the quotient

==================================================================

Theory  
Now the question is interesting as they have written the quotient as a decimal number. Now, lets understand that using a simple example first
 
⦿ 20 when divided by 4 gives 5 as quotient, that's straight forward right.
⦿ 20 when divided by 3 gives 6 as quotient and 2 as remainder, that's easy too
⦿ Now, 20 when divided by 3 gives 6.67 (approx.) as quotient. Now this is what they mean when they say that x/y quotient is 15.15 in option 1.
⦿ Lets go bit deeper into this, this means that 20 when divided by 3 gives 0.67 * 3 as remainder, which is nothing but 2
⦿ So, 0.67*3 will be the remainder

==================================================================

Now, with that context lets attempt the problem.

I.  \frac{x}{y}   quotient is 15.15 => 0.15*y = 60 => y =  \frac{60}{0.15}  => y = 400 =>   POSSIBLE   as y is integer

II.  \frac{x}{y}   quotient is 18.16 => 0.16*y = 60 => y =  \frac{60}{0.16}  => y = 375 =>   POSSIBLE   as y is integer

III.  \frac{x}{y}   quotient is 17.17 => 0.17*y = 60 => y =  \frac{60}{0.17}  => y = 352.3 =>   NOT Possible   as y is NOT an integer

So,  I and II are correct

So,  Answer will be D 
Hope it helps!

1) Remainders Basics

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

2) Remainders Advanced

https://www.youtube.com/watch?v=h1HTEhmUb1w

Kinshook · Answer

When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?

I. 15.15 : .15y = 60; y=60/.15 =400 ; feasible 
II. 18.16 : .16y = 60; y=60/.16=375 ; feasible 
III. 17.17 : .17y = 60; y=60/.17=352.941; not feasible since y is an integer

(A) I only 
(B) II only 
(C) III only 
(D) I and II only 
(E) I and III only

IMO D

When the integer x is divided by the integer y, the remainder is 60.

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When the integer x is divided by the integer y, the remainder is 60.

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