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# Set A contains all of the integers from 100 to 200, inclusive. Set B

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Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129001 [0], given: 12187

Set A contains all of the integers from 100 to 200, inclusive. Set B [#permalink]

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28 Aug 2017, 23:35
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Difficulty:

35% (medium)

Question Stats:

75% (01:51) correct 25% (02:14) wrong based on 53 sessions

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Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925
[Reveal] Spoiler: OA

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Kudos [?]: 129001 [0], given: 12187

Math Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1527

Kudos [?]: 952 [0], given: 72

Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)
Re: Set A contains all of the integers from 100 to 200, inclusive. Set B [#permalink]

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29 Aug 2017, 01:49
Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925

Sum of Set A minus the sum of set B = Sum of integers from 126 to 200 - Sum of integers from 25 to 99 (Since integers 100 to 125 are common in both sets , we exclude them )
= 75/2 * (126+200) - 75/2 *(25+99)
= 75/2 ( 326 - 124)
= 75 * 202/2
= 75*101
= 7575

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+1 Kudos if you find this post helpful

Kudos [?]: 952 [0], given: 72

Director
Joined: 22 May 2016
Posts: 818

Kudos [?]: 266 [0], given: 552

Set A contains all of the integers from 100 to 200, inclusive. Set B [#permalink]

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29 Aug 2017, 08:52
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Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925

I thought about excluding common terms, but decided the arithmetic might be easier if I did not.

1) Sum of Set A

200 - 100 = 100 + 1 = 101 terms

$$\frac{200+100}{2}$$ * 101 = (150)(101)

2) Sum of Set B

125 - 100 = 100 + 1 = 101 terms

$$\frac{125+25}{2}$$ * 101 = (75)(101)

3) Sum of A - Sum of B =

(150)(101) - (75)(101)

101(150 - 75) =
101(75) =
(100 + 1)(75)

7500 + 75 = 7575

Kudos [?]: 266 [0], given: 552

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 837 [0], given: 5

Re: Set A contains all of the integers from 100 to 200, inclusive. Set B [#permalink]

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01 Sep 2017, 12:02
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925

Since we see there is overlap between sets, we can just determine the sum of the integers from 25 to 99 inclusive and 126 to 200 inclusive. Remember average = (first number + last number)/2.

For set B (excluding 100 to 125 inclusive):

sum = avg x quantity

sum = (25 + 99)/2 x (99 - 25 + 1)

sum = 62 x 75

For set A (excluding 100 to 125 inclusive):

sum = avg x quantity

sum = (126 + 200)/2 x (200 - 126 + 1)

sum = 163 x 75

Thus, A - B = 163 x 75 - 62 x 75 = 75(163 - 62) = 75(101) = 7,575.

Alternate solution:

Even though some of the numbers in B overlap with those in A, we can just find the sum of all the numbers in B and subtract that from the sum of all the numbers in A.

We use the formulas sum = average x quantity and average = (first number + last number)/2.

For set B:

sum = avg x quantity

sum = (25 + 125)/2 x (125 - 25 + 1)

sum = 75 x 101

For set A:

sum = avg x quantity

sum = (100 + 200)/2 x (200 - 100 + 1)

sum = 150 x 101

Thus, A - B = 150 x 101 - 75 x 101 = 101(150 - 75) = 101(75) = 7,575.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 837 [0], given: 5

Re: Set A contains all of the integers from 100 to 200, inclusive. Set B   [#permalink] 01 Sep 2017, 12:02
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