GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 12:04 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Set X consists of the first 100 positive even integers. Set Y consists

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  B
Joined: 02 Mar 2016
Posts: 5
Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

1
10 00:00

Difficulty:   75% (hard)

Question Stats: 65% (03:22) correct 35% (02:56) wrong based on 164 sessions

HideShow timer Statistics

Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500
Senior SC Moderator V
Joined: 14 Nov 2016
Posts: 1348
Location: Malaysia
Re: Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

4
1
Matruco wrote:
Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500

Official solution from Veritas Prep.

This problem heavily rewards you for knowing how to quickly calculate the sum of an evenly-spaced set. When you look at the two sets, you have:

$$Set X$$: $$2, 4, 6, 8, 10….198, 200$$
$$Set Y$$: $$5, 10, 15, 20…495, 500$$

And note that you do not need to perform a “count” to make sure you have exactly 100 terms in each set. Multiples of 2 are defined as 2 times an integer, so the first 100 terms will be 1 * 2, 2 * 2, 3 * 2… up to 100 * 2. Same for multiples of 5: 1 * 5, 2 * 5, 3 * 5…100 * 5. So you know that your ending number for each set will be 100 times the common multiple.
When you’re dealing with evenly-spaced set, the median equals the mean. So you can quickly calculate the average by averaging the first and last term. For Set X, that’s $$\frac{(2 + 200)}{2} = 101$$, and for Set Y that’s $$\frac{(5 + 500)}{2} = 252.5$$.

Now you’ll use the Average = Sum of Terms / Number of Terms rule to your advantage. The sum of the terms (what you want) can be calculated by multiplying the average times the number of terms. So for Set X that’s 100(101) = 10100. And for Set Y that’s 100(252.5) = 25250.

At this point you can sum those two sets to arrive at 35350. But wait – the question specified “unique terms” and “no repeat elements.” So here you will have to subtract out the numbers that are multiples of both 2 and 5. Which are those? The multiples of 10.

But be careful: Here you do not have 100 multiples of 10; you only have the multiples of 10 up to 200 (where the set of even numbers stops). So you’ll calculate the multiples of 10 between 10 and 200, inclusive. Again, take the average (105) and multiply by the number of terms (20) to get 2100. When you subtract that from 35350 you’ll have the correct answer, 33250.
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

General Discussion
Senior Manager  G
Joined: 24 Apr 2016
Posts: 321
Re: Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

2
1
Sum of first 100 positive even integers: 2 + 4 + 6 + 8 + ....+ 200 = [100 (2+200)]/2 = 10100

Sum of first 100 positive multiples of 5: 5 + 10 + 15 + ... + 500 = [100 (5+500)]/2 = 25250

Sum of multiples of 10 till 200: 10 + 20 + 30 + ... + 200 = [20 (10+200)]/2 = 2100

Therefore: Sum of all unique terms in the new set = 10100 + 25250 - 2100 = 33250 (A)
Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Re: Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

Matruco wrote:
Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500

Similar question: https://gmatclub.com/forum/set-x-consis ... 86754.html
_________________
Manager  S
Joined: 03 Jan 2017
Posts: 134
Re: Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

find sum of 100 even intergers
find sum of 100 multiplies of 5
and then deduct the sum of multiplies of 10 from 10 to 200
10100+25250-2100=33250 (A)
Senior Manager  S
Joined: 08 Jun 2015
Posts: 420
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33
Re: Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

+1 for option A.

First find sum of all multiples of 2 = 10100
Next, find sum of all multiples of 5 = 25250

Sum of all common numbers = 2100

The final value = 35350-2100 = 33250.

Option A it is
_________________
" The few , the fearless "
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: Set X consists of the first 100 positive even integers. Set Y consists  [#permalink]

Show Tags

1
Matruco wrote:
Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500

The sum of the numbers in X is (2 + 200)/2 x 100 = 202 x 50 = 10,100. Similarly, the sum of the numbers in Y is (5 + 500)/2 x 100 = 505 x 50 = 25,250. When the two sets of numbers are combined into one single set, if duplicate elements (i.e., the elements that are common in both sets) count as twice, then the sum of the new set would be 10,100 + 25,250 = 35,350. However, since the duplicate elements should only count once, not twice, we need to subtract, from 35,350, the sum of the duplicate elements. The duplicate elements are 10, 20, …, 200, with a sum of (10 + 200)/2 x 20 = 210 x 10 = 2,100. So the sum of the new set when the duplicate elements only count once is 35,350 - 2,100 = 33,250.

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Set X consists of the first 100 positive even integers. Set Y consists   [#permalink] 20 Aug 2018, 11:52
Display posts from previous: Sort by

Set X consists of the first 100 positive even integers. Set Y consists

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  