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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
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When the integer x is divided by the integer y, the remainder is 60.
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18 May 2021, 01:01
18 May 2021, 01:01
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Question Stats:
40% (02:43) correct
60% (02:22) wrong based on 130 sessions
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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
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
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When the integer x is divided by the integer y, the remainder is 60.
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21 May 2021, 06:44
21 May 2021, 06:44
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
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
==================================================================
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) GRE Lesson: Remainders Basics (PSAT\SAT\ACT\GMAT\GRE\Bank PO)
2) GRE Lesson: Remainders Advanced
You can read more about Remainders in this post.
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) GRE Lesson: Remainders Basics (PSAT\SAT\ACT\GMAT\GRE\Bank PO)
2) GRE Lesson: Remainders Advanced
You can read more about Remainders in this post.
General Discussion
Re: When the integer x is divided by the integer y, the remainder is 60.
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03 Jan 2025, 08:44
03 Jan 2025, 08:44
1
For this specific question, could we also solve it using the following approach:
1. 15.15 can be written as 15 + 15/100. Since remainder is 60 and 60 is a multiple of 15 this can be one of the possibilities if we multiply 15/100*4
2. Second option can also be written as 18 + 16/100, if 16/100 is simplified further this can be written in the form 4/25 and again 60 is a multiple of 4 so this is also one of the possibilities
3. 17 + 17/100 cannot be simplified further and 60 is not its multiple so this can never be a possibility
Can we use the following approach to arrive at the answer? Is this reasoning correct? It would be great if someone could confirm. Thank you!
1. 15.15 can be written as 15 + 15/100. Since remainder is 60 and 60 is a multiple of 15 this can be one of the possibilities if we multiply 15/100*4
2. Second option can also be written as 18 + 16/100, if 16/100 is simplified further this can be written in the form 4/25 and again 60 is a multiple of 4 so this is also one of the possibilities
3. 17 + 17/100 cannot be simplified further and 60 is not its multiple so this can never be a possibility
Can we use the following approach to arrive at the answer? Is this reasoning correct? It would be great if someone could confirm. Thank you!
