John and Ingrid pay 30% and 40% tax annually, respectively. : GMAT Problem Solving (PS)
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# John and Ingrid pay 30% and 40% tax annually, respectively.

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Veritas Prep GMAT Instructor
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John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink]

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18 Jan 2011, 20:08
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65% (02:54) correct 35% (02:15) wrong based on 375 sessions

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John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes$72000, what is their combined tax rate?

A. 32%
B. 34.4%
C. 35%
D. 35.6%
E. 36.4%

It is one of my favorite problems from the Veritas Arithmetic book.. I like to use Weighted Averages here...
[Reveal] Spoiler: OA

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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 18 Oct 2010 Posts: 92 Followers: 2 Kudos [?]: 8 [2] , given: 0 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 19 Jan 2011, 00:19 2 This post received KUDOS (0.3*56000+0.4*72000)/(72000+56000)=0.35625 D thank you Manager Joined: 27 Jul 2010 Posts: 197 Location: Prague Schools: University of Economics Prague Followers: 1 Kudos [?]: 41 [1] , given: 15 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 19 Jan 2011, 02:14 1 This post received KUDOS It would be good to specify whether they the salary they make is already taxed or not. But anyway, is there any way to solve (0.3*56000+0.4*72000)/(72000+56000)=0.35625 in hand? _________________ You want somethin', go get it. Period! Intern Joined: 16 Mar 2010 Posts: 13 Followers: 0 Kudos [?]: 3 [2] , given: 3 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 19 Jan 2011, 06:49 2 This post received KUDOS Code: Income TAX J - 56,000 16,800 I - 72,000 28,800 ----------------------- T- 128,000 45,600 Part X ----- = ------ Whole 100 45,600 X -------- = ----- 128,000 100 45,600 * 100 X = -------------- 128,000 4560 X = ------ = 35.6 128 short cut 4560 4560 456 X = ------ =(approx) ------- = ---- = 35.07 128 130 13 As denominator has been increased answer choice should be greater than 35.07 So the Ans is 35.6% Manager Joined: 11 Jul 2009 Posts: 175 WE: Design (Computer Software) Followers: 1 Kudos [?]: 50 [1] , given: 62 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 19 Jan 2011, 08:44 1 This post received KUDOS i go with D (0.3*56000+0.4*72000)/(72000+56000)=0.35625 _________________ Kaustubh Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7076 Location: Pune, India Followers: 2088 Kudos [?]: 13300 [10] , given: 222 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 19 Jan 2011, 18:50 10 This post received KUDOS Expert's post 9 This post was BOOKMARKED John and Ingrid pay 30% and 40% tax annually, respectively. If John makes$56000 and Ingrid makes $72000, what is their combined tax rate? a. 32% b. 34.4% c. 35% d. 35.6% e. 36.4% Great solution everyone! Yes, the answer is (D) 35.6. Now let me explain why I like this question. The big numbers - 56000 and 72000 have limited utility. I could have as well given 86380 and 111060 as their salaries; I would have still obtained the same answer! We need to find the weighted average of their tax rate. The important thing is their individual tax rates and the ratio of their salaries 7:9 (56000:72000), not the actual salaries Attachment: Ques1.jpg [ 3.44 KiB | Viewed 6655 times ] The length between 30% and 40% i.e. 10% is split in the ratio 9:7. So the average will be at (9/16)*10 + 30 = 35.6%. So you don't have to do any long calculations. If there is a doubt in this method, check out this link: http://gmatclub.com/forum/tough-ds-105651.html#p828579 When we want to find the average of lets say age of 2 groups - one group has average age of 30 yrs and there are 10 people in it and the other group has average age of 40 yrs and there are 40 people in it, all we need is the relative weights (relative number of people) in the two groups i.e. 1:4. It doesn't matter whether there are 10 and 40 people or 100 and 400 people... It's exactly the same concept here. Let me know if there is a doubt in this concept. and when we say, "A makes$100,000," we mean gross by default. Taxes are a part of your salary just like your other expenses.
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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 27 Jul 2010 Posts: 197 Location: Prague Schools: University of Economics Prague Followers: 1 Kudos [?]: 41 [0], given: 15 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 20 Jan 2011, 01:46 Thank you Karishma, your method is very strong indeed. Little bit reoulsive on the first look, but great when mastered. VeritasPrepKarishma wrote: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes$56000 and Ingrid makes $72000, what is their combined tax rate? a. 32% b. 34.4% c. 35% d. 35.6% e. 36.4% Great solution everyone! Yes, the answer is (D) 35.6. Now let me explain why I like this question. The big numbers - 56000 and 72000 have limited utility. I could have as well given 86380 and 111060 as their salaries; I would have still obtained the same answer! We need to find the weighted average of their tax rate. The important thing is their individual tax rates and the ratio of their salaries 7:9 (56000:72000), not the actual salaries Attachment: Ques1.jpg The length between 30% and 40% i.e. 10% is split in the ratio 9:7. So the average will be at (9/16)*10 + 30 = 35.6%. So you don't have to do any long calculations. If there is a doubt in this method, check out this link: http://gmatclub.com/forum/tough-ds-105651.html#p828579 When we want to find the average of lets say age of 2 groups - one group has average age of 30 yrs and there are 10 people in it and the other group has average age of 40 yrs and there are 40 people in it, all we need is the relative weights (relative number of people) in the two groups i.e. 1:4. It doesn't matter whether there are 10 and 40 people or 100 and 400 people... It's exactly the same concept here. Let me know if there is a doubt in this concept. and when we say, "A makes$100,000," we mean gross by default. Taxes are a part of your salary just like your other expenses.

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You want somethin', go get it. Period!

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Re: A Problem from Veritas Arithmetic Book [#permalink]

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22 Jun 2011, 11:12
Hi Karishma,

I really love the weighted averages shortcut method you use every time,but I get confused in using it.

Thanks!

regards,
Veritas Prep GMAT Instructor
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Re: A Problem from Veritas Arithmetic Book [#permalink]

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23 Jun 2011, 03:17
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dkj1984 wrote:
Hi Karishma,

I really love the weighted averages shortcut method you use every time,but I get confused in using it.

Thanks!

regards,

When we use the formula of weighted averages, we say that one quantity is A1 and its weight is w1. Another is A2 and its weight is w2. We have to find the average Aavg.
The formula is w1/w2 = (A2 - Aavg)/(Aavg - A1)

Notice that you have w1 in numerator on LHS and A2 in numerator on RHS.
Check out these posts on how the formula is derived and how it is used:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/
_________________

Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 20 Dec 2010 Posts: 258 Schools: UNC Duke Kellogg Followers: 4 Kudos [?]: 40 [0], given: 4 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 23 Jun 2011, 10:35 Nice shortcut method!!...Great! Intern Joined: 28 Mar 2011 Posts: 34 Followers: 0 Kudos [?]: 2 [0], given: 0 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 24 Jun 2011, 20:52 Hi Karishma, Thanks a ton! terrific explanation in the links provided. Regards, Intern Joined: 28 Apr 2012 Posts: 18 Followers: 0 Kudos [?]: 11 [0], given: 51 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 11 Dec 2012, 01:24 VeritasPrepKarishma wrote: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes$56000 and Ingrid makes $72000, what is their combined tax rate? a. 32% b. 34.4% c. 35% d. 35.6% e. 36.4% Great solution everyone! Yes, the answer is (D) 35.6. Now let me explain why I like this question. The big numbers - 56000 and 72000 have limited utility. I could have as well given 86380 and 111060 as their salaries; I would have still obtained the same answer! We need to find the weighted average of their tax rate. The important thing is their individual tax rates and the ratio of their salaries 7:9 (56000:72000), not the actual salaries Attachment: Ques1.jpg The length between 30% and 40% i.e. 10% is split in the ratio 9:7. So the average will be at (9/16)*10 + 30 = 35.6%. So you don't have to do any long calculations. If there is a doubt in this method, check out this link: http://gmatclub.com/forum/tough-ds-105651.html#p828579 When we want to find the average of lets say age of 2 groups - one group has average age of 30 yrs and there are 10 people in it and the other group has average age of 40 yrs and there are 40 people in it, all we need is the relative weights (relative number of people) in the two groups i.e. 1:4. It doesn't matter whether there are 10 and 40 people or 100 and 400 people... It's exactly the same concept here. Let me know if there is a doubt in this concept. and when we say, "A makes$100,000," we mean gross by default. Taxes are a part of your salary just like your other expenses.

I am lost at (9/16)*10 + 30 = 35.6%. where YOU add 30. I want to learn how to use this method completely so I can have it in my back pocket ready to use. I feel that we already found the ratio and then flipped it so it would be the distance and could put it in the chart. We divided 9/16 to find the middle number that was missing and multiplied by 10 because that was the weight? Is the only reason because 10+30 = the original 40?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7076
Location: Pune, India
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Re: A Problem from Veritas Arithmetic Book [#permalink]

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11 Dec 2012, 23:31
dcastan2 wrote:
I am lost at (9/16)*10 + 30 = 35.6%. where YOU add 30. I want to learn how to use this method completely so I can have it in my back pocket ready to use. I feel that we already found the ratio and then flipped it so it would be the distance and could put it in the chart. We divided 9/16 to find the middle number that was missing and multiplied by 10 because that was the weight? Is the only reason because 10+30 = the original 40?

The distance between 30 and 40 i.e. 10 has to be split in the ratio 9:7. The average is 9 (of these 16 units) to the right of 30. So you find 9/16th of 10 which is 90/16 and add it to 30.

Before you work on this question, check out the links mentioned in the post above. I have discussed simpler numbers in them. They will give you a feel for the method. Thereafter, you can solve any question using this method.
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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 25 Kudos [?]: 415 [0], given: 11 Re: A Problem from Veritas Arithmetic Book [#permalink] ### Show Tags 18 Dec 2012, 22:21 Using weighted averages... (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35. (2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range. (3) Get 72000/128000 = 72/128 = 9/16. 9/16 is a little above 8/16 = 1/2. Thus, our answer is just a little above 35. Answer: D For details on Weighted Averages: Weighted Averages _________________ Impossible is nothing to God. MBA Section Director Affiliations: GMAT Club Joined: 21 Feb 2012 Posts: 3722 Location: India City: Pune GMAT 1: 680 Q49 V34 GPA: 3.4 WE: Business Development (Manufacturing) Followers: 379 Kudos [?]: 2783 [3] , given: 1961 Re: John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink] ### Show Tags 18 Aug 2013, 10:04 3 This post received KUDOS Expert's post 4 This post was BOOKMARKED Here is another approach Attachments Untitled.png [ 51.62 KiB | Viewed 3728 times ] _________________ Senior Manager Joined: 10 Jul 2013 Posts: 335 Followers: 3 Kudos [?]: 306 [0], given: 102 Re: John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink] ### Show Tags 18 Aug 2013, 12:15 VeritasPrepKarishma wrote: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes$56000 and Ingrid makes $72000, what is their combined tax rate? A. 32% B. 34.4% C. 35% D. 35.6% E. 36.4% It is one of my favorite problems from the Veritas Arithmetic book.. I like to use Weighted Averages here... (0.3 * 56000 + 0.4 * 72000) / (72000 + 56000) = 0.356 = 35.6% = D (Answer) _________________ Asif vai..... Current Student Joined: 06 Sep 2013 Posts: 2035 Concentration: Finance GMAT 1: 770 Q0 V Followers: 60 Kudos [?]: 582 [0], given: 355 Re: John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink] ### Show Tags 29 Dec 2013, 06:53 VeritasPrepKarishma wrote: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes$56000 and Ingrid makes $72000, what is their combined tax rate? A. 32% B. 34.4% C. 35% D. 35.6% E. 36.4% It is one of my favorite problems from the Veritas Arithmetic book.. I like to use Weighted Averages here... Ratio is 56/72 = 8/9 Weighted average is therefore ((30)(8) + (40)(9))/17 = 600/17=35.6% Hence answer is D Hope it helps Cheers! J Manager Joined: 11 Sep 2013 Posts: 153 Concentration: Finance, Finance Followers: 2 Kudos [?]: 90 [0], given: 156 Re: John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink] ### Show Tags 08 May 2014, 01:21 ratio of their salaries 7:9 (56000:72000) 30 40 X 40-x x-30 (40-x):(x-30) = 7: 9 X= 35.6% GMAT Club Legend Joined: 09 Sep 2013 Posts: 12903 Followers: 562 Kudos [?]: 158 [0], given: 0 Re: John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink] ### Show Tags 28 May 2015, 23:51 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ SVP Joined: 17 Jul 2014 Posts: 2091 Location: United States (IL) Concentration: Finance, Economics Schools: Stanford '19 GMAT 1: 550 Q39 V27 GMAT 2: 560 Q42 V26 GMAT 3: 560 Q43 V24 GMAT 4: 650 Q49 V30 WE: General Management (Transportation) Followers: 18 Kudos [?]: 248 [0], given: 124 Re: John and Ingrid pay 30% and 40% tax annually, respectively. [#permalink] ### Show Tags 11 Apr 2016, 17:50 VeritasPrepKarishma wrote: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes$56000 and Ingrid makes $72000, what is their combined tax rate? a. 32% b. 34.4% c. 35% d. 35.6% e. 36.4% Great solution everyone! Yes, the answer is (D) 35.6. Now let me explain why I like this question. The big numbers - 56000 and 72000 have limited utility. I could have as well given 86380 and 111060 as their salaries; I would have still obtained the same answer! We need to find the weighted average of their tax rate. The important thing is their individual tax rates and the ratio of their salaries 7:9 (56000:72000), not the actual salaries Attachment: Ques1.jpg The length between 30% and 40% i.e. 10% is split in the ratio 9:7. So the average will be at (9/16)*10 + 30 = 35.6%. So you don't have to do any long calculations. If there is a doubt in this method, check out this link: http://gmatclub.com/forum/tough-ds-105651.html#p828579 When we want to find the average of lets say age of 2 groups - one group has average age of 30 yrs and there are 10 people in it and the other group has average age of 40 yrs and there are 40 people in it, all we need is the relative weights (relative number of people) in the two groups i.e. 1:4. It doesn't matter whether there are 10 and 40 people or 100 and 400 people... It's exactly the same concept here. Let me know if there is a doubt in this concept. and when we say, "A makes$100,000," we mean gross by default. Taxes are a part of your salary just like your other expenses.

I always get messed up when trying to use this method...ended up the direct one...
56,000 = 100%
5,600=10%
11,200 = 20%
28,000 = 50%
16800 = 30%

72,000 = 100%
36,000 = 50%
7,200 = 10%
28,800 = 40%

now..
28,800+16,800=45600
total amount: 128,000

45,600/128,000 = 456/1280 = 228/640 = 114/320 = 57/160. clearly it is more than 33% since 60/180 is 1/3 or 33%. A is out right away...
now...long division....
57/160 = 0.35625

so 35.625%

closest one: D
Re: John and Ingrid pay 30% and 40% tax annually, respectively.   [#permalink] 11 Apr 2016, 17:50
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