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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pm; Thanked: 29 times; Followed by:4 members

number system

by vipulgoyal » Fri Jun 07, 2013 3:41 am

What is the reminder when the positive integer x is
divided by 8 ?
1. when x is divided by 12 the rermindr is 5
2. when x is divided by 18 ther eminder is 7

Ans E

Normally I do these type of qustions by counting
like
1. 5,17,29,41,53,65,77......
2. 7,25,43,61,79,97,115.....

after getting common no(not any in this qustion) from 1 & 2 divide by the required no( in this qustion 8) to get the reminder
Experts please suggest, is there any other way round to solve these kind of qustions bit quicker??

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Source: Beat The GMAT — Problem Solving | Fri Jun 07, 2013 3:41 am

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 am; Location: Seattle, WA; Thanked: 86 times; Followed by:2 members

by srcc25anu » Fri Jun 07, 2013 10:04 am

I think the Second statement meant to say: when x is divided by 18, the remainder is 11

If so, the question becomes is x divisible by 8?

ST1: x can be 5, 17, 29 ... and remainder would be 5, 1 and 5 respectively
Not Sufficient

ST2: x can be 11, 29, 47 ... and remainder would be 3, 5 and 7 respectively
Not sufficient

Together 1 and 2: if we extend both the series above, we have 29 and 65 that will satisfy both statement 1 and statement 2. But the remainder for 29/8 = 5 and Rem (65/8) = 1
Both statement together are also Insufficient.
E

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Jun 08, 2013 5:36 am

vipulgoyal wrote:What is the remainder when the positive integer x is divided by 8 ?
1. when x is divided by 12 the remainder is 5
2. when x is divided by 18 the remainder is 11"

NOTE: srcc25anu is right - statement 2, should read "when x is divided by 18 the remainder is 11"

Target question: What is the remainder when the positive integer x is divided by 8 ?

Statement 1: When x is divided by 12 the remainder is 5
When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for statement 1, the possible values of x are 5, 17, 29, 41, . . .
Let's examine two possible values of x:
Case a: x = 5, in which case x divided by 8 leaves remainder 5
Case b: x = 17, in which case x divided by 8 leaves remainder 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: when x is divided by 18 the remainder is 11
So, the possible values of x are 11, 29, 47, 65, . . .
Let's examine two possible values of x:
Case a: x = 11, in which case x divided by 8 leaves remainder 3
Case b: x = 29, in which case x divided by 8 leaves remainder 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We're now looking for values of x that satisfy statement 1 AND statement 2
From statement 1, x could equal 5, 17, 29, 41, 65, 77 . . .
From statement 2, x could equal 11, 29, 47, 65, 83, . . .
As you might guess, there are several possible values of x. Let's examine two of them:
Case a: x = 29, in which case x divided by 8 leaves remainder 5
Case b: x = 65, in which case x divided by 8 leaves remainder 1
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pm; Thanked: 29 times; Followed by:4 members