Pluggin in answers vs number properties

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JJMforthegold: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Tue Aug 29, 2017 8:07 pm

Pluggin in answers vs number properties

by JJMforthegold » Sun Sep 17, 2017 7:16 pm

Experts-

With this question, I know i can just plug in the answers but is there other rules we need to know for the gmat?

For which of the following values of n is (100+n)/n NOT an integer?

a) 1
b) 2
c) 3
d) 4
e) 5
c

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Source: Beat The GMAT — Problem Solving | Sun Sep 17, 2017 7:16 pm

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by [email protected] » Sun Sep 17, 2017 8:59 pm

Hi JJMforthegold,

TESTing THE ANSWERS is a perfect approach for this type of question - simply plug in the options until you find the one that 'fits' what the prompt describes. There are some Number Properties involved in this question that might help you on other prompts though, so I'll review them here:

101/1 = 101 Dividing an integer by 1 will always lead to the same integer (you probably knew this one already)

102/2 = 51 Dividing any even integer by 2 will always lead to an integer

103/3 = 34 1/3 To determine whether an integer is evenly divisible by 3 or not, you can use the 'rule of 3' (if the DIGITS of the number sum to a total that is divisible by 3, then the number is divisible by 3). For example:
27 IS divisible by 3 because 2+7 = 9. Since 9 is divisible by 3, 27 is divisible by 3.
26 is NOT divisible by 3 because 2+6 = 8. Since 8 is not divisible by 3, 26 is not divisible by 3.

Here, we're dealing with 103. 1+0+3 = 4. Since 4 is not divisible by 3, 103 is not divisible by 3.

104/4 = 26 If the last 2 digits of a number for a 2-digit number that is divisible by 4, then the larger number is divisible by 4.
For example:
104 is divisible by 4 because 04 is divisible by 4.
126 is NOT divisible by 4 because 26 is not divisible by 4.

105/5 = 21 If an integer ends in 5 (or 0), then dividing that integer by 5 will always lead to an integer.

Final Answer: C

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

Contact Rich at [email protected]

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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 » Mon Sep 18, 2017 7:34 am

JJMforthegold wrote:For which of the following values of n is (100+n)/n NOT an integer?

a) 1
b) 2
c) 3
d) 4
e) 5
c

The GMAT loves to test the following rule:
(a + b)/c = a/c + b/c

Applying this rule, we get: (100+n)/n = 100/n + n/n = 100/n + 1
In order for 100/n + 1 to be an integer, it must be the case that 100/n is an integer.
In order for 100/n to be an integer, n must be a factor of 100
So, we can eliminate all answer choices that are factors of 100
So, ELIMINATE A, B, D and E

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon Mar 12, 2018 10:36 am

JJMforthegold wrote:Experts-

With this question, I know i can just plug in the answers but is there other rules we need to know for the gmat?

For which of the following values of n is (100+n)/n NOT an integer?

a) 1
b) 2
c) 3
d) 4
e) 5

This problem is easiest solved by plugging in each answer choice.

A) (100 + 1)/1 = 101/1 = 101

Answer choice A yields an integer.

B) (100 + 2)/2 = 102/2 = 51

Answer choice B yields an integer.

C) (100 + 3)/3 = 103/3 = 34 2/3

Answer choice C DOES NOT yield an integer.

Although we believe answer choice C is correct, we should still test the other answer choices.

D) (100 + 4)/4 = 104/4 = 26

Answer choice D yields an integer.

E) (100 + 5)/5 = 105/5 = 21

Answer choice E yields an integer.

Alternate solution:

Notice that (100 + n)/n = 100/n + n/n = 100/n + 1. The only way this will not be an integer is if n is not a factor of 100. Looking at the choices, we see that 3 is not a factor of 100, so the answer is C.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]