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# When n is divided by 5 the remainder is 2. When n is divided

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Math Expert
Joined: 02 Sep 2009
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Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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15 Jul 2013, 00:00
From 100 hardest questions
Bumping for review and further discussion.
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Concentration: Strategy, Technology
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Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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12 Mar 2014, 02:14
yezz wrote:
When n is divided by 5 the remainder is 2. When n is divided by 7 the remainder is 1. If n is less than 800 , how many values of n are possible?

A. 22
B. 23
C. 24
D. 25
E. 26

It is not mentioned in the question that n must be positive.
If n is allowed to take negative values, then there are infinite solutions.
Else, 23. (B)
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Joined: 01 May 2017
Posts: 12
Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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03 Jun 2017, 02:38
When n is divided by 5 the remainder is 2. When n is divided by 7 the remainder is 1. If n is less than 800 , how many values of n are possible?

When n is divided by 5 the remainder is 2
N=5A+2--E1

When n is divided by 7 the remainder is 1.

N=7B+1--E2

EQUATE THEM E1X7=E1X5
35A+14=35B+5
35A-35B+14-5
35(A-B)+9
35C+9<800
C=22
VALUE OF C CAN BE 0 ALSO
HENCE 22+1=23

IS IT CORRECT WAY
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Joined: 07 Dec 2014
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When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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Updated on: 08 Dec 2017, 16:54
1
yezz wrote:
When n is divided by 5 the remainder is 2. When n is divided by 7 the remainder is 1. If n is less than 800 , how many values of n are possible?

A. 22
B. 23
C. 24
D. 25
E. 26

n=5q+2
n=7p+1
5q+1=7p
least value of q=4
least value of n=22
let x=possible values of n<800
22+(x-1)(5*7)<800
x<23.2
x=23
B

Originally posted by gracie on 03 Jun 2017, 21:59.
Last edited by gracie on 08 Dec 2017, 16:54, edited 1 time in total.
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Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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27 Jun 2017, 22:02
We know that the First common term is 22.

LCM (5,7) = 35. This means the difference between current term and next term will be 35.

We have series 22, 22+35 = 57, 57+22 = 97, ..........

As per the condition given in question n< 800.
Let's say n = 798 (To keep the calculation easy).

We know that formula to find consecutive term with constant increment is

$$\frac{(Last - First )}{increment} + 1$$

therefore, $$\frac{(798 - 22)}{35} + 1$$

$$\frac{776}{35} + 1$$

22.17 + 1 = 23.17 = 23

Ans : B
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Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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23 Sep 2018, 06:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: When n is divided by 5 the remainder is 2. When n is divided &nbs [#permalink] 23 Sep 2018, 06:03

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