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# Math: Number Theory - Percents

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Manager
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Re: Math: Number Theory - Percents [#permalink]

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21 Jun 2010, 18:29
Excellent resources!

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22 Jun 2010, 19:32
Thanks for the effort and good work! Kudos.

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22 Jun 2010, 19:34
thanks for sharing!

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11 Jul 2010, 02:48
Hello Bunnel,

This is indeed very helpful. Can you please also add a few examples containing cost price, marked price and selling price scenarios.
Thanks

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21 Jul 2010, 23:33
Compound Interest

$$Balance(final)=$$
$$=principal*(1+\frac{interest}{C})^{time*C}$$, where C = the number of times compounded annually.

If C=1, meaning that interest is compounded once a year, then the formula will be: $$Balance(final)=$$
$$principal*(1+interest)^{time}$$, where time is number of years.

Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: $$Balance=20,000*(1+\frac{0.12}{4})^{2*4}=$$ $$=20,000*(1.03)^8=25,335.4$$ I dont understand why 0.12/4 ? where did we get no 4 ? thanks Kudos [?]: 26 [0], given: 17 Manager Joined: 09 Jun 2010 Posts: 71 Kudos [?]: 26 [0], given: 17 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 22 Jul 2010, 07:09 thanks bunnel But one more question, when it says compunded semiannually, does it mean half ? for example 6 ? do we take 3 ? thanks Kudos [?]: 26 [0], given: 17 Manager Joined: 27 May 2010 Posts: 197 Kudos [?]: 71 [0], given: 3 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 02 Aug 2010, 20:59 The Probability material is really helpful thanks... Kudos [?]: 71 [0], given: 3 Intern Joined: 02 Sep 2009 Posts: 16 Kudos [?]: 2 [0], given: 13 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 06 Aug 2010, 06:47 Thanks for your efforts Kudos [?]: 2 [0], given: 13 Intern Joined: 01 Oct 2010 Posts: 4 Kudos [?]: [0], given: 1 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 09 Oct 2010, 14:30 Generic questions based on percentages that can be remembered: 1. If the price(p) of an Item increases by x% then consumption(c) has to be decreased by 100 /(100+x) % to keep the expenditure(E) constant. 2. If two articles are sold at same price , and on first one the shopkeeper makes a profit of p% and on the other suffers a loss of p % , overall he suffers a loss. The loss is p*p /100 % ie., ( p square divided by 100). Especially,I have seen the second type of question very common one in many competitive tests. Note : Please let me know if you are interested in the reason behind each answer. This is my first post in gmatclub.I thank all of the gmatclub members / moderators for providing such a wonderful environment. Kudos [?]: [0], given: 1 Intern Joined: 21 Oct 2010 Posts: 5 Kudos [?]: [0], given: 0 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 23 Oct 2010, 06:32 Hey guys i am new in this forum... can you help me with these percentage problem? 1) The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. THe percentage slump in business is: i)1 ii) 8 iii) 20 iv)80 2) p is 6 times as large as q. The percent that q is less than p is: i) 83.33 ii) 16.5 iii) 90 iv) 60 3) In a market survey 20% voted for A and 60% voted for B. the remaining were uncertain. if the difference between who voted for B and those who were uncertain was 720 how many individuals were covered in the survey? i) 3600 ii) 1440 iii)1800 iv) cant determine Kudos [?]: [0], given: 0 Senior Manager Status: Not afraid of failures, disappointments, and falls. Joined: 20 Jan 2010 Posts: 290 Kudos [?]: 260 [0], given: 260 Concentration: Technology, Entrepreneurship WE: Operations (Telecommunications) Re: Math: Number Theory - Percents [#permalink] ### Show Tags 23 Oct 2010, 07:21 syenaman wrote: Generic questions based on percentages that can be remembered: 1. If the price(p) of an Item increases by x% then consumption(c) has to be decreased by 100 /(100+x) % to keep the expenditure(E) constant. 2. If two articles are sold at same price , and on first one the shopkeeper makes a profit of p% and on the other suffers a loss of p % , overall he suffers a loss. The loss is p*p /100 % ie., ( p square divided by 100). Especially,I have seen the second type of question very common one in many competitive tests. Note : Please let me know if you are interested in the reason behind each answer. This is my first post in gmatclub.I thank all of the gmatclub members / moderators for providing such a wonderful environment. Would love the explanation with some nice examples. _________________ "I choose to rise after every fall" Target=770 http://challengemba.blogspot.com Kudos?? Kudos [?]: 260 [0], given: 260 Intern Joined: 03 Nov 2010 Posts: 1 Kudos [?]: [0], given: 0 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 13 Nov 2010, 07:29 Thanks guys...found what i was looking for...you are wonderful.. Kudos [?]: [0], given: 0 Manager Joined: 01 Apr 2010 Posts: 164 Kudos [?]: 16 [0], given: 6 Re: Math: Number Theory - Percents [#permalink] ### Show Tags 16 Nov 2010, 05:52 Bunuel wrote: PERCENTS This post is a part of [GMAT MATH BOOK] created by: Bunuel edited by: bb, walker -------------------------------------------------------- This topic is included in GMAT ToolKit App (iPhone/iPod Touch) [read more] [AppStore] -------------------------------------------------------- Definition A percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, "%", or the abbreviation "pct". Since a percent is an amount per 100, percents can be represented as fractions with a denominator of 100. For example, 25% means 25 per 100, 25/100 and 350% means 350 per 100, 350/100. • A percent can be represented as a decimal. The following relationship characterizes how percents and decimals interact. Percent Form / 100 = Decimal Form For example: What is 2% represented as a decimal? Percent Form / 100 = Decimal Form: 2%/100=0.02 Percent change General formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$ Example: A company received$2 million in royalties on the first $10 million in sales and then$8 million in royalties on the next $100 million in sales. By what percent did the ratio of royalties to sales decrease from the first$10 million in sales to the next $100 million in sales? Solution: Percent decrease can be calculated by the formula above: $$Percent=\frac{Change}{Original}*100=$$ $$=\frac{\frac{2}{10}-\frac{8}{100}}{\frac{2}{10}}*100=60%$$, so the royalties decreased by 60%. Simple Interest Simple interest = principal * interest rate * time, where "principal" is the starting amount and "rate" is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate. Example: If$15,000 is invested at 10% simple annual interest, how much interest is earned after 9 months?
Solution: $15,000*0.1*9/12 =$1125

Compound Interest

$$Balance(final)=$$
$$=principal*(1+\frac{interest}{C})^{time*C}$$, where C = the number of times compounded annually.

If C=1, meaning that interest is compounded once a year, then the formula will be: $$Balance(final)=$$
$$principal*(1+interest)^{time}$$, where time is number of years.

Example: If \$20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year?
Solution: $$Balance=20,000*(1+\frac{0.12}{4})^{2*4}=$$
$$=20,000*(1.03)^8=25,335.4$$

Percentile

If someone's grade is in $$x_{th}$$ percentile of the $$n$$ grades, this means that $$x%$$ of people out of $$n$$ has the grades less than this person.

Example: Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

Solution:
Being in 80th percentile out of 120 grades means Lena outscored $$120*0.8=96$$ classmates.

In another class she would outscored $$200-24=176$$ students.

So, in combined classes she outscored $$96+176=272$$. As there are total of $$120+200=320$$ students, so Lena is in $$\frac{272}{320}=0.85=85%$$, or in 85th percentile.

Official GMAC Books:

The Official Guide, 12th Edition: PS #10; PS #17; PS #19; PS #47; PS #55; PS #60; PS #64; PS #78; PS #92; PS #94; PS #109; PS #111; PS #115; PS #124; PS #128; PS #131; PS #151; PS #156; PS #166; PS #187; PS #193; PS #200; PS #202; PS #220; DS #2; DS #7; DS #21; DS #37; DS #48; DS #55; DS #61; DS #63; DS #78; DS #88; DS #92; DS #120; DS #138; DS #142; DS #143;

Generated from [GMAT ToolKit]

[Reveal] Spoiler:
Attachment:
Math_icon_percents.png

In the compound interest example, Please let me know how do we calculate 20000*(1.03)^8 . is there any simple way to find (1.03)^8.

thanx....

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Re: Math: Number Theory - Percents [#permalink]

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02 Aug 2011, 21:11
redwine01 wrote:
Hey guys i am new in this forum... can you help me with these percentage problem?

1) The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. THe percentage slump in business is:

i)1 ii) 8 iii) 20 iv)80

2) p is 6 times as large as q. The percent that q is less than p is:

i) 83.33 ii) 16.5 iii) 90 iv) 60

3) In a market survey 20% voted for A and 60% voted for B. the remaining were uncertain. if the difference between who voted for B and those who were uncertain was 720 how many individuals were covered in the survey?

i) 3600 ii) 1440 iii)1800 iv) cant determine

Hi Guys!

Thank you.

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Re: Math: Number Theory - Percents [#permalink]

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10 Aug 2011, 04:06
1)iii 20
Lets say initial income=x, amended income=y then 4x/100=5y/100 ie x/y=5/4
If income declines from 5 to 4, its 20% decrease.

2)i 83.33
p=6q ie p/q=6/1 therefore p-q/p=6-1/6=5/6=83.33%

3)iii 1800
Votes for A=20%, B=60%, uncertain(U)=20% and B-U=60%-20%=720 ie 40%=720 ie 100%=1800

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Re: Math: Number Theory - Percents [#permalink]

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12 Feb 2012, 01:07
Bunuel wrote:
gurpreetsingh wrote:
Bunuel wrote:
PERCENTS

Example: Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

Solution:
Being in 80th percentile out of 120 grades means Lena outscored $$120*0.8=96$$ classmates.

In another class she would outscored $$200-24=176$$ students.

So, in combined classes she outscored $$96+176=272$$. As there are total of $$120+200=320$$ students, so Lena is in $$\frac{272}{320}=0.85=85%$$, or in 85th percentile.

[Reveal] Spoiler:
Attachment:
Math_icon_percents.png

In another class she would outscored $$200-24=176$$ students.
I think it should be 200-24-1 = 175 as 24 were higher than Lena , thus 24+1 are lower than her, we need to count her as well

The point here is that Lena herself is not in the other class. So in another class she outscored 200-24=176 not 175.

Hope it's clear.

But the question does not say Lena is not in other class. So, how to interpret this, based on the provided solutions?
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Re: Math: Number Theory - Percents [#permalink]

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12 Feb 2012, 02:23
"Lena’s grade was in the 80th percentile out of 120 grades in HER class. In ANOTHER class ..." So another class is not Lena's class.
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Re: Math: Number Theory - Percents [#permalink]

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12 Feb 2012, 04:19
Bunuel wrote:
"Lena’s grade was in the 80th percentile out of 120 grades in HER class. In ANOTHER class ..." So another class is not Lena's class.

OK. Thanks.
I observed that, but I looked at those two statements "independently", because we are not allowed to make assumptions unless sufficient supporting material is available.
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Re: Math: Number Theory - Percents [#permalink]

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12 Feb 2012, 04:23
Chembeti wrote:
Bunuel wrote:
"Lena’s grade was in the 80th percentile out of 120 grades in HER class. In ANOTHER class ..." So another class is not Lena's class.

OK. Thanks.
I observed that, but I looked at those two statements "independently", because we are not allowed to make assumptions unless sufficient supporting material is available.

It's a PS question, so sentences are not independent like the statements in DS. Check similar GMAT Prep problem: amy-s-grade-was-90th-percentile-of-the-80-grades-for-her-98164.html

Hope it helps.
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Re: Math: Number Theory - Percents [#permalink]

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12 Feb 2012, 04:50
Bunuel wrote:
Chembeti wrote:
Bunuel wrote:
"Lena’s grade was in the 80th percentile out of 120 grades in HER class. In ANOTHER class ..." So another class is not Lena's class.

OK. Thanks.
I observed that, but I looked at those two statements "independently", because we are not allowed to make assumptions unless sufficient supporting material is available.

It's a PS question, so sentences are not independent like the statements in DS. Check similar GMAT Prep problem: amy-s-grade-was-90th-percentile-of-the-80-grades-for-her-98164.html

Hope it helps.

Yes, it helped me lot, Bunnel. I thank you very much. Now, I realized the difference between PS && DS. (shame on me )
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Re: Math: Number Theory - Percents   [#permalink] 12 Feb 2012, 04:50

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