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M31-33

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M31-33  [#permalink]

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New post 14 Jun 2015, 13:39
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If \(x\) is a positive integer and 123 divided by \(x\) leaves a remainder of 3, what is the value of \(x\)?


(1) The remainder when 60 is divided by \(x\) is more than or equal to 60.

(2) \(x\) is a multiple of 60

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Re M31-33  [#permalink]

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New post 14 Jun 2015, 13:39
Official Solution:


If \(x\) is a positive integer and 123 divided by \(x\) leaves a remainder of 3, what is the value of \(x\)?

The stem says that 123 is 3 more than a multiple of 3: \(123 = xq + 3\), which gives \(120= xq\). Therefore \(x\) must be a factor of 120 greater than 3 (divisor, \(x\), must be more than the remainder 3). So, \(x\) can be: 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 or 120.

(1) The remainder when 60 is divided by \(x\) is more than or equal to 60. The remainder, cannot be greater than the dividend, thus the remainder remainder when 60 is divided by \(x\) IS 60. Which implies that \(x\) is greater than 60. Hence \(x = 120\). Sufficient.

(2) \(x\) is a multiple of 60. From above \(x\) can be 60 or 120. Not sufficient.


Answer: A
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Re: M31-33  [#permalink]

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New post 29 Mar 2017, 05:35
Hi Brunel,

Can you please elaborate on why x must be more than the remainder 3 ? I was not able to understand the same.
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Re: M31-33  [#permalink]

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New post 29 Mar 2017, 05:51
varunjoshi31 wrote:
Hi Brunel,

Can you please elaborate on why x must be more than the remainder 3 ? I was not able to understand the same.


Because the remainder (3 in our case) is always less than divisor (x in our case).

Check the links below for more:
Theory on remainders problems
Tips on remainders

DS remainders problems
PS remainders problems

Hope it helps.
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Collection of Questions:
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Re: M31-33  [#permalink]

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New post 08 Jan 2019, 00:18
can you please elaborate on statement 1.How can a divisor be more than a dividend and still leave a remainder?
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Re: M31-33  [#permalink]

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New post 08 Jan 2019, 00:29
Dannys wrote:
can you please elaborate on statement 1.How can a divisor be more than a dividend and still leave a remainder?


Let me ask you a question: how many leftover apples would you have if you had 60 apples and wanted to distribute in 120 baskets evenly? Each basket would get 0 apples and 120 apples would be leftover (remainder).

So, when a divisor is more than dividend, then the remainder equals to the dividend, for example:
3 divided by 4 yields the reminder of 3: \(3=4*0+3\);
9 divided by 14 yields the reminder of 9: \(9=14*0+9\);
1 divided by 9 yields the reminder of 1: \(1=9*0+1\).

For more on this check:

5. Divisibility/Multiples/Factors




6. Remainders



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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M31-33  [#permalink]

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New post 08 Jan 2019, 00:46
Bunuel wrote:
If \(x\) is a positive integer and 123 divided by \(x\) leaves a remainder of 3, what is the value of \(x\)?


(1) The remainder when 60 is divided by \(x\) is more than or equal to 60.

(2) \(x\) is a multiple of 60


Given x +ive Integer
123/x gives Remainder =3

x can be any of these values 6,40,60,120

Statement 1
Remainder when 60/x is > or = 60

This is only possible when x =120, because if you take other values from the sample set,
60/40, Remainder = 20
60/6, Remainder= 0
60/60, Remainder= 0
60/120, Remainder= 60

Statement 2
x can be 60,120,240
Will give 2 values for x, 60 and 120.

Only Statement 1 is sufficient for answering the question

Answer A
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Re: M31-33 &nbs [#permalink] 08 Jan 2019, 00:46
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