Tens digit

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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 amFollowed by: 5 members; Thanked: 28 times

by gmatblood » Fri Nov 04, 2011 10:51 am

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What is the tens digt of positive integer x
(1) x divided by 100 has a remainder of 30
(2) x divided by 110 has a remander of 30

IMO: A

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 04, 2011 10:51 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Fri Nov 04, 2011 11:05 am

1.
x divided by 100 , remainder 30
x = 130, 230, 330, 430,....

Tens digit = 3

Sufficient

2.
x divided by 110, remainder 30
x= 140,250,360,...
Tens digit = 4/5/6/...

Insufficient

Option A

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

by Brent@GMATPrepNow » Sat Nov 05, 2011 5:33 am

gmatblood wrote:What is the tens digt of positive integer x
(1) x divided by 100 has a remainder of 30
(2) x divided by 110 has a remander of 30

IMO: A

As rijul007 showed, listing possible values of x is a great approach here.

To answer questions involving remainders, it's useful to be able to list possible values. So, here's the rule for this:

If N/D has remainder R, then the possible values of N = R, R+D, R+2D, R+3D, . . .
Note: N,D and R are non-negative integers.

Example: If N divided by 7 has remainder 3, then the possible values of N are as follows: 3, 10, 17, 24, 31, 38, etc

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Apr 08, 2018 3:05 pm

Hi All,

We're told that X is a positive integer. We're asked for the TENS DIGIT of X. This question can be solved by TESTing VALUES.

1) X divided by 100 has a remainder of 30

IF....
X = 30, then 30/100 = 0 r 30 and the answer to the question is 3
X = 130, then 130/100 = 1 r 30 and the answer to the question is 3
X = 230, then 230/100 = 2 r 30 and the answer to the question is 3
Etc.
Based on the information in Fact 1, the answer to the question is ALWAYS 3.
Fact 1 is SUFFICIENT

2) X divided by 110 has a remander of 30

IF....
X = 30, then 30/110 = 0 r 30 and the answer to the question is 3
X = 140, then 140/110 = 1 r 30 and the answer to the question is 4
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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