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# P, a positive integer, leaves remainder 83 when divided by 120. What

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P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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24 Oct 2017, 23:06
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65% (hard)

Question Stats:

56% (02:06) correct 44% (01:52) wrong based on 93 sessions

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P, a positive integer, leaves remainder 83 when divided by 120. What is the remainder when 3P -­ 300 is divided by 40?

A. 3
B. 9
C. 11
D. 29
E. 31

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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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24 Oct 2017, 23:37
2
1
Take a value larger than 120 which will leave a remainder of 83
Eg. 120+83 = 203

3 x 203 - 300 = 309

Nearest multiple of 40 to 309 is 280 / Just find the remainder of 309 divided by 40

Hence the answer is 309 - 280 = 29
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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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25 Oct 2017, 02:02
Jagdeesh wrote:
Take a value larger than 120 which will leave a remainder of 83
Eg. 120+83 = 203

3 x 203 - 300 = 309

Nearest multiple of 40 to 309 is 280 / Just find the remainder of 309 divided by 40

Hence the answer is 309 - 280 = 29

Hi, I don't understand, please explain!
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P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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25 Oct 2017, 02:32
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1
Sprincejindal wrote:
Jagdeesh wrote:
Take a value larger than 120 which will leave a remainder of 83
Eg. 120+83 = 203

3 x 203 - 300 = 309

Nearest multiple of 40 to 309 is 280 / Just find the remainder of 309 divided by 40

Hence the answer is 309 - 280 = 29

Hi, I don't understand, please explain!

From Stem, P = 120n+83

now,
= 3(120n+83) -300 divided by 40
= 360n+249-300
= 360n-51

here 360n should be divided by 40
so -51 divided by 40 means 29 should be the reminder.

Note: observe that the sign is -51(minus) remainder 11 is a trap answer.
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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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25 Oct 2017, 03:04
How -51 divided by 40 leaves a remainder of 29?

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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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25 Oct 2017, 03:19
tiger66 wrote:
How -51 divided by 40 leaves a remainder of 29?

Sent from my iPhone using GMAT Club Forum

-51, it should be 80 - 51, hope you get it.
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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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25 Oct 2017, 09:31
1
Sprincejindal wrote:
Jagdeesh wrote:
Take a value larger than 120 which will leave a remainder of 83
Eg. 120+83 = 203

3 x 203 - 300 = 309

Nearest multiple of 40 to 309 is 280 / Just find the remainder of 309 divided by 40

Hence the answer is 309 - 280 = 29

Hi, I don't understand, please explain!

The idea is to find a number that satisfies the question stem. Hence choose a number 'p' that will satisfy the condition.

p / 120 should leave a remainder of 83. Let's assume that the quotient is 1,

p = 120*1 + 83 = 203.

Now, plug in the remainder of the question:

3 * p - 300 = 609 - 300 = 309.

Divide 309 by 40 which will leave a remainder of 29.

Hope this helps.
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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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29 Oct 2017, 07:24
nkmungila wrote:
P, a positive integer, leaves remainder 83 when divided by 120. What is the remainder when 3P -­ 300 is divided by 40?

A. 3
B. 9
C. 11
D. 29
E. 31

We can create the equation P = 120Q + 83

When Q = 1, P = 120 + 83 = 203.

Thus, 3P - 300 = 3(203) - 300 = 309.

309/40 = 7 remainder 29

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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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29 Oct 2017, 07:34
nkmungila wrote:
P, a positive integer, leaves remainder 83 when divided by 120. What is the remainder when 3P -­ 300 is divided by 40?

A. 3
B. 9
C. 11
D. 29
E. 31

Hi..
40 is a factor of 120
if P leaves a remainder 83 when div by 120, it will leave a remainder of 3 when div by 40....

lets see 3P-300..
3P will leave a remainder of 3*3=9
and -300 will leave a remainder of 20 as -300 = -4*80+20
.... Always remember there is NO negative remainder
total remainder = 9+20=29
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Re: P, a positive integer, leaves remainder 83 when divided by 120. What  [#permalink]

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01 Nov 2017, 06:31
nkmungila wrote:
Sprincejindal wrote:
Jagdeesh wrote:
Take a value larger than 120 which will leave a remainder of 83
Eg. 120+83 = 203

3 x 203 - 300 = 309

Nearest multiple of 40 to 309 is 280 / Just find the remainder of 309 divided by 40

Hence the answer is 309 - 280 = 29

Hi, I don't understand, please explain!

From Stem, P = 120n+83

now,
= 3(120n+83) -300 divided by 40
= 360n+249-300
= 360n-51

here 360n should be divided by 40
so -51 divided by 40 means 29 should be the reminder.

Note: observe that the sign is -51(minus) remainder 11 is a trap answer.

We can can 83 as p.
In that case the remainder is 9

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Re: P, a positive integer, leaves remainder 83 when divided by 120. What &nbs [#permalink] 01 Nov 2017, 06:31
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