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# What is the remainder when positive integer x is divided by 5?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 05:04
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5% (low)

Question Stats:

82% (00:56) correct 18% (01:35) wrong based on 156 sessions

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What is the remainder when positive integer x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 05:54
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1
Bunuel wrote:
What is the remainder when x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

1) statement one tells us that the last digit is 7... so the remainder when divided by x will always be 2.. suff
2) statement two tells us that it is an odd number.. not suff
ans A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 06:11
1
method..,

From Option A: X= 10K+7 => X= (5*2K+ 5)+2 => 5 (2K+1)+2 /5.

The remainder will be 2 always. Sufficient

From Option B: X= 2k+1 (Substituting K=1, 2 and 3 gives X= 3, 5, 7 and each have remainders -- 3, 0 and 2 respectively.

Not sufficient.

Option A.

Bunuel wrote:
What is the remainder when x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

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Kudos to you, for helping me with some KUDOS.

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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 08:37
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Bunuel wrote:
What is the remainder when x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

My attempt:

To know the remainder of X/5, we must know the unit digit of Y.

Statement 1 - x divided by 10 has a remainder of 7
This means, unit digit of X is 7. So X/5 Will always leave remainder as 2

Hence Statement 1 is sufficient.

Statement 2 - x divided by 2 has a remainder of 1.
In this case unit digit can be any odd number, accordingly remainder of X/5 will differ.

Say for Example
Unit digit of X is 1, X/5 will leave Remainder as 1
Unit digit of X is 3, X/5 will leave Remainder as 3
Unit digit of X is 5, X/5 will leave Remainder as 0
Unit digit of X is 7, X/5 will leave Remainder as 2
Unit digit of X is 9, X/5 will leave Remainder as 4

Hence statement 2 is not sufficient.

Hence Option A is correct
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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 08:51
1
(1) x divided by 10 has a remainder of 7.

From this information we can determine that x has unit digit of 7. {7, 27, 37, 47, ....etc }

Thus, any no having unit digit as 7 when divided by 5 gives remainder as 2. {117, 157, 1037, .....etc}

Hence, the information is sufficient to answer the question What is the remainder when x is divided by 5. It is 2 always

(2) x divided by 2 has a remainder of 1.

From this we can determine that X is odd number {3,5,7,9,11}

When 5 is divided by 5, then remainder is zero. But when 7 is divided by 5, then remainder is 2.

Different ans hence, insufficient

So, Ans is A
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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 09:32
1
What is the remainder when x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Solution -

Statement1 - For values of x=7, 17, 27, 37,.... when divided by 10, remainder is 7.

When the same sequence of above numbers divided by 5, remainder is 2. Sufficient.

Statement2 - For values of x=1,3,5,7,9,....... when divided by 2, remainder is 1.

When the same sequence is divided by 5, results multiple remainders are 1,3,1,2,4,..... In Sufficient.

Thanks

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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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17 Jun 2015, 10:17
1
using statement 1 alone , values can be 7,17,27,37..... If any of these value is divided by 5 reminder will always be 2. So sufficient

Using statement 2 alone , Values can be 1,3,5,7,9,11 .... if you divide any of these numbers , reminder willl keep changing - so insufficient .

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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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18 Jun 2015, 23:12
Bunuel wrote:
What is the remainder when x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

1: x has a units digit of 7, so the remainder when x is divided by 5 will be 2. Sufficient.
2: x is odd. Tells us nothing about the remainder when x is divided by 5. Insufficient.
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Posts: 53063
Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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22 Jun 2015, 05:01
Bunuel wrote:
What is the remainder when x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Statement 2 is easier to evaluate—INSUFFICIENT. Any odd number will have a remainder of 1 when divided by 2. 3 ÷ 5 has a remainder of 3, but 5 ÷ 5 has a remainder of 0.

Statement 1, however, is SUFFICIENT. If x divided by 10 has a remainder of 7, then the units digit of x is 7. Such numbers are all 2 greater than a multiple of 5, so when x is divided by 5 the remainder is 2.

The correct answer is (A): Statement 1 ALONE is sufficient, but Statement 2 ALONE is not sufficient.

Attachment:

2015-06-22_1700.png [ 16.32 KiB | Viewed 1756 times ]

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Re: What is the remainder when positive integer x is divided by 5?  [#permalink]

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19 Oct 2018, 13:31
Bunuel wrote:
What is the remainder when positive integer x is divided by 5?

(1) x divided by 10 has a remainder of 7.
(2) x divided by 2 has a remainder of 1.

Kudos for a correct solution.

x/10 = q + 7/10

x = 10q + 7

x = 7,17,27 etc..

7/5 = 1 2/5
17/5 = 3 2/5

Sufficient.

Eliminate B/C/E.

Statement 2)

x = 1,3,5,7 etc..

1/5
3/5
5/5
7/5 = 1 2/5

Insufficient.

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Re: What is the remainder when positive integer x is divided by 5?   [#permalink] 19 Oct 2018, 13:31
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