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

Question

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

Jagdeesh · Accepted Answer

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

nkmungila · Answer

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.

Sprincejindal · Answer

Hi, I don't understand, please explain!

tiger66 · Answer

How -51 divided by 40 leaves a remainder of 29?

Sent from my iPhone using GMAT Club Forum

nkmungila · Answer

-51, it should be 80 - 51, hope you get it.

Jagdeesh · Answer

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.

JeffTargetTestPrep · Answer

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

Answer: D

chetan2u · Answer

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

saifulbio · Answer

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

Posted from my mobile device

Abhishek009 · Answer

The least value of P = 83 , when divided by 120 leaves a remainder of 83

Now, 3P - 300 is 3*83 - 300 = -51

Now, when divided by 40 remainder will be 51 - 40 = 9 , Answer must be (B) 9

krndatta · Answer

EducationAisle

How do we solve this using the minus sign? 
Please explain

Sandeepgurwa · Answer

Step 1 : for 3P remainder = 83 ×3 = 249
Step 2 : 3P - 300 remainder = 249 - 300 = -51
Step 3 : minus cannot be remainder. Therefore, subtract it from original divisor 120. You will get 69 remainder.
Step 4 : Comes to the last part of question what is the remainder when divided by 40. Clearly, we can se that in 69 when divided by 40 remainder is 29. So that is the answer. 🙂

siddharth_ · Answer

I was confused about the following -
-51 = 40*-1 -11
-51 = 40*-2 + 29
Now, which one should we consider? Asked ChatGPT about the same. Attaching my prompt and its reply here.

prompt - "from gmat perspective, what is the remainder when -51 is divided by 40". 
reply in screenshot.
Essentially it said -- Remainder can't be negative and hence 29 is the correct answer.

chetan2u · Answer

Both are correct as final answer will be 29 in both cases. 
-51=40×(-1)-11, so remainder becomes -11. But remainder cannot be negative so 
-11=40×(-1)+29. Hence remainder is 29

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

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