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GRE Quant: Arithmetic [#permalink]
When p is divided by 7, the remainder is 4. When p is divided by 4, the remainder is 1. How many different values of p are less than 120?
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Re: When p is divided by 7, the remainder is 4. When p is divide [#permalink]
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Merged similar topics.

Follow the rules for posting on the board AND post a question along with the answer choices NOT only the question.

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Re: When p is divided by 7, the remainder is 4. When p is divide [#permalink]
I think this type of problem is common in the exam. good one
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Re: When p is divided by 7, the remainder is 4. When p is divide [#permalink]
Given that When p is divided by 7, the remainder is 4. When p is divided by 4, the remainder is 1. And we need to find How many different values of p are less than 120

Theory: Dividend = Divisor*Quotient + Remainder

When p is divided by 7, the remainder is 4

p -> Dividend
7 -> Divisor
a -> Quotient (Assume)
4 -> Remainders
=> p = 7*a + 4 = 7a + 4

When p is divided by 4, the remainder is 1

p -> Dividend
4 -> Divisor
b -> Quotient (Assume)
1 -> Remainders
=> p = 4*b + 1 = 4b + 1

p = 7a + 4 = 4b + 1
=> b = \(\frac{7a + 3}{4}\)

Only those values of "a" which will also give "b" as integer will give us the common values of p
a = 3, 7, 11, 15, 19,...
But a = 19 will give us a value of > 120 for p

=> 4 value of p which are less than 120 are possible

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: When p is divided by 7, the remainder is 4. When p is divide [#permalink]
Hello from the GRE Prep Club BumpBot!

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