December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2285

Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
21 Sep 2018, 03:08
Question Stats:
58% (03:22) correct 42% (03:05) wrong based on 149 sessions
HideShow timer Statistics
eGMAT Question of the Week #15Set S contains all the integers from 10 to 99. \(S_1\), a subset of S, contains all the numbers of S, in which both the digits are even. \(S_2\), also a subset of S, contains all the numbers of S, in which both the digits are odd. What is the ratio of sum of all elements in \(S_1\) to sum of all elements in \(S_2\)? A. \(\frac{108}{275}\)
B. \(\frac{216}{275}\)
C. \(\frac{2}{3}\)
D. \(\frac{275}{216}\)
E. \(\frac{3}{2}\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




Intern
Joined: 03 Sep 2018
Posts: 5

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
25 Sep 2018, 08:59
Analysis (20 seconds): Looks like I need to find the size of each set, use the sum of a series formula to find their respective sums and simplify the fraction. I also notice that the numerators of the answer choices are distinct so I'll be focussing on reducing the numerator until I see a match.
Strategy: Find n for both sets, Calculate sum of each series, Reduce the fraction focussing on the numerator
Find n (40 seconds) S1 > n = 4 * 5 = 20, first element = 20, last = 88 S2 > n = 5 * 5 = 25, first element = 11, last = 99
Calculate sums (45 seconds) \(Sum = \frac{n(a1 + an)}{2}\) \(S1 = \frac{20(20 + 88)}{2} = 10 * 108\) \(S2 = \frac{25(11 + 99)}{2} = \frac{25 * 110}{2} = 25 * 11 * 5\)
Reduce & Eliminate (30 seconds) \(\frac{10 * 108}{25 * 11 * 5} = \frac{2 * 108}{25 * 11} = \frac{216}{...}\)
Answer = B Total Time: 2:15




Manager
Joined: 23 Aug 2016
Posts: 108
Location: India
Concentration: Finance, Strategy
GPA: 2.84
WE: Other (Energy and Utilities)

Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
21 Sep 2018, 03:42
EgmatQuantExpert wrote: eGMAT Question of the Week #15Set S contains all the integers from 10 to 99. \(S_1\), a subset of S, contains all the numbers of S, in which both the digits are even. \(S_2\), also a subset of S, contains all the numbers of S, in which both the digits are odd. What is the ratio of sum of all elements in \(S_1\) to sum of all elements in \(S_2\)? A. \(\frac{108}{275}\)
B. \(\frac{216}{275}\)
C. \(\frac{2}{3}\)
D. \(\frac{275}{216}\)
E. \(\frac{3}{2}\) Quite a lengthy One! Set S1= { 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62,64,66,68,80,82,84,86,88}= Sum(1080) Set S2={ 11, 13,15,17,31,33,35,37,39,51,53,55,57,59,71,73,75,77,79,91,93,95,97,99}= Sum(1375) Sum of S1/Sum of S2= 1080/1375= 216/275. Answer B
_________________
Thanks and Regards,
Honneeey.
In former years,Used to run for "Likes", nowadays, craving for "Kudos". :D



Intern
Joined: 08 Apr 2018
Posts: 16

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
24 Sep 2018, 02:06
Answer would be 'B'.
Within {0 ... 9}, the even digits would be {0, 2, 4, 6 and 8} and similarly the odd digits would be {1, 3, 5, 7, 9}
Here, since we are referring to 2 sets, S1 where both the digits are even, hence all of the numbers which are going to be included will contain both the digits from {0, 2, 4, 6, 8}.
... and for S2, where it contains all the numbers of S, in which both the digits are odd, hence all of the numbers which are going to be included will contain both the digits from {1, 3, 5, 7, 9}.
S1 would contain the following sets  {20, 22, 24, 26, 28} , {40, 42, 44, 46, 48} , {60, 62 , 64, 66, 68} and {80, 82, 84, 86, 88}
Similarly, S2 would be containing the following  {11, 13, 15, 17, 19} , {31, 33, 35, 37, 39} , {51, 53, 55, 57, 59} , {71, 73, 75, 77, 79} and {91, 93, 95, 97, 99}
All of the individual sets within S1 and S2 is having the same common difference as 2 and the number of terms as 5. Utilizing the formula for a sequence in arithmetic progression, we would be able to determine the sum of the indivual series and add those up to determine the final sum.
S1 = 5/2 [ 40 + (4*2) ] + 5/2 [ 80 + (4*2) ] + 5/2 [ 120 + (4*2) ] + 5/2 [ 160 + (4*2) ] = 120 + 220 + 320 + 420 = 1080 S2 = 5/2 [ 22 + (4*2) ] + 5/2 [ 62 + (4*2) ] + 5/2 [ 102 + (4*2) ] + 5/2 [ 142 + (4*2) ] + 5/2 [ 182 + (4*2) ] = 75 + 175 + 275 + 375 + 475 = 1375
Now, we are being asked to determine the ratio of the sum of all elements in S1 to the sum of all elements in S2.
S1 / S2 = 1080/1375 = 216 / 275



Intern
Joined: 07 Jan 2012
Posts: 15
Location: Canada
Concentration: International Business, Entrepreneurship
GMAT Date: 04302012
WE: Information Technology (Computer Software)

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
25 Sep 2018, 18:17
honneeey wrote: EgmatQuantExpert wrote: eGMAT Question of the Week #15Set S contains all the integers from 10 to 99. \(S_1\), a subset of S, contains all the numbers of S, in which both the digits are even. \(S_2\), also a subset of S, contains all the numbers of S, in which both the digits are odd. What is the ratio of sum of all elements in \(S_1\) to sum of all elements in \(S_2\)? A. \(\frac{108}{275}\)
B. \(\frac{216}{275}\)
C. \(\frac{2}{3}\)
D. \(\frac{275}{216}\)
E. \(\frac{3}{2}\) Quite a lengthy One! Set S1= { 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62,64,66,68,80,82,84,86,88}= Sum(1080) Set S2={ 11, 13,15,17,31,33,35,37,39,51,53,55,57,59,71,73,75,77,79,91,93,95,97,99}= Sum(1375) Sum of S1/Sum of S2= 1080/1375= 216/275. Answer B Quick question  can't see 19 am I missing something?



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2285

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
25 Sep 2018, 22:45
Solution Given:• Set S contains all the integers from 10 to 99, both inclusive
o \(S_1\), contains all the numbers of set S, in which both the digits are even o \(S_2\), contains all the numbers of set S, in which both the digits are odd To find:• \(\frac{Sum of all elements in S_1}{Sum of all elements in S_2}\) Approach and Working: \(S_1\) = {20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88} • The sum of first set of five elements in \(S_1\) = 20 + 22 + 24 + 26 + 28
o (2*10) + (2*10 + 2) + (2*10 + 4) + (2*10 + 6) + (2*10 + 8) = 2*10*5 + (2 + 4 + 6 + 8) = 120 • The sum of next set of five elements in \(S_1\)= 40 + 42 + 44 + 46 + 48
o Now, if we compare the elements in the first and second set of 5 numbers each, we can see that each element in the second set is 20 more than the corresponding element in the first set. o Thus, we can write the sum of the five elements in the second set = the sum of the five elements in the first set + 20*5 = 120 + 100 = 220 • Similarly, the sum of next set of five elements = sum of the five elements in the second set + 20 * 5 = 220 + 100 = 320 • And, the sum of last set of five elements = 320 + 100 = 420 Thus, sum of all elements in \(S_1\) = 120 + 220 + 320 + 420 = 1080 \(S_2\) = {11, 13, 15, 17, 19, 31, 33, 35, 37, 39, 51, 53, 55, 57, 59, 71, 73, 75, 77, 79, 91, 93, 95, 97, 99} • Sum of first five elements in \(S_2\) = 11 + 13 + 15 + 17 + 19
o (10 + 1) + (10 + 3) + (10 + 5) + (10 + 7) + (10 + 9) = 10*5 + (1 + 3 + 5 + 7 + 9) = 75 • The sum of next five elements in \(S_2\)= 31 + 33 + 35 + 37 + 39
o Which can be written as (11+ 20) + (13 + 20) + (15 + 20) + (17 + 20) + (19 + 20) o (11 + 13 + 15 + 17 + 19) + 20*5 = 75 + 100 = 175
• Similarly, the sum of next five elements = 175 + 100 = 275 • And, the sum of next five elements = 275 + 100 = 375 • And, the sum of last five elements = 375 + 100 = 475 Thus, sum of all elements in \(S_2\) = 75 + 175 + 275 + 375 + 475 = 75*5 + 1000 = 1375 Therefore, \(\frac{S_1}{S_2} = \frac{1080}{1375} = \frac{216}{275}\) Hence, the correct answer is option B. Answer: B
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Manager
Joined: 28 Jun 2018
Posts: 61

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
02 Oct 2018, 08:40
jameslewis could you explain a little clearly how you derived N? Isn't N suppose to be the intervals between the sequence? In this case how would you find that?



Manager
Joined: 28 Jun 2018
Posts: 61

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
02 Oct 2018, 08:45
jameslewis sorry, N is number of terms, but doesn't the AS formula only apply when the increase or decrease is by the same amount? How did we apply it here then? More importantly, how did it work??? chetan2u >>??



Manager
Joined: 14 Jun 2018
Posts: 213

Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
02 Oct 2018, 09:46
I think this might be the quickest way
Even : 20 , 22 , 24, 26 , 28. 40 , 42 , 44, 46 ,48 60... 80... The mean of each group is 24 , 44 , 64 , 84 The mean of the entire set is (44+64) / 2 = 54 Therefore , the sum of the set is 54*4*5 = 1080 (4= no of group ; 5 = no of terms in each group)
Do the same for odd 11 , 13 , 15 , 17 , 19 31.. 51.. 71.. 91..
The mean of the set will be 55 The sum of the entire set is 55*5*5 = 1375 (Here total number of group is 5 and each group has 5 terms)
Required ratio = 1080/1375 = 216/275



Intern
Joined: 18 Jul 2018
Posts: 14

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
22 Oct 2018, 22:02
Hi JAMES, I see you have used the AP formula to do the calculation but neither is S1 nor S2 in arithmetic progression from what I understand. S1 20,22,24,26,28,40,42....can you please explain.Thankyou..



Intern
Joined: 17 Dec 2017
Posts: 15
Location: United States

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
26 Oct 2018, 14:47
hibobotamuss wrote: jameslewis sorry, N is number of terms, but doesn't the AS formula only apply when the increase or decrease is by the same amount? How did we apply it here then? More importantly, how did it work??? chetan2u >>?? chetan2u I am also stumped on why we were able to apply this formula here. It is my understanding that N(Last + First)/2 only works with sets consisting of evenly spaced integers. Could you please help explain it's application here?



Intern
Joined: 21 Aug 2018
Posts: 3

Re: Question of the Week 15 (Set S contains all the integers from 10...)
[#permalink]
Show Tags
27 Oct 2018, 05:56
This is how i solved (hopefully it's right) S1: 20, 22, 24, 26, 28 (even spaced set => mean = median = 24) => Sum = 24*5 4.... 6... 8... S2: 11, 13, 15, 17, 19, same as above => Sum = 15*5 3... 5... 7... 9....
Just dont do any calculation yet. S1/S2 = (24*5 + 44*5 + 64*5 + 84*5) /(15*5 + 35*5 + 55*5 + 75*5 + 95*5)
Cancel 5 and quickly you can identify the last digit of the numerator (6) and the denominator (5) => C
Double check by actually do the calculation if you want




Re: Question of the Week 15 (Set S contains all the integers from 10...) &nbs
[#permalink]
27 Oct 2018, 05:56






