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

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

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New post 15 Jul 2013, 01:00
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Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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New post 12 Mar 2014, 03:14
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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Re: When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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New post 03 Jun 2017, 03:38
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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When n is divided by 5 the remainder is 2. When n is divided  [#permalink]

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New post Updated on: 08 Dec 2017, 17:54
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, 22:59.
Last edited by gracie on 08 Dec 2017, 17:54, 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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New post 27 Jun 2017, 23:02
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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New post 23 Sep 2018, 07:03
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Re: When n is divided by 5 the remainder is 2. When n is divided &nbs [#permalink] 23 Sep 2018, 07:03

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