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Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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01 Apr 2013, 20:50

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Great idea. This is probably a great way to ingrain things for question writers. My Quant strength is exponents, so I'll get things started with one of those:

If \(\frac{4^{3x}}{16^{3x/2}} = (2)(2^{-3x})\), what is x?

A) x = 1/3 B) x = 2/3 C) x = 1 D) x = 3/2 E) x = 3

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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02 Apr 2013, 03:02

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For the 2008 season, a certain sports league had eight teams. For the 2010 season, the number of teams was increased to ten. In a season, each team plays exactly two matches with each of the other teams. If the revenue per match for the 2008 season was $1 million and the revenue per match for the 2010 season was $1.25 million, what was the percentage increase in total revenues from all matches from the 2008 season to the 2010 season?

Explanation : We know, \(a^3\) +\(b^3\) + \(c^3\) = 3abc if a+b+c = 0. Here a+b+c = 97 - 57 - 40 = 0. So, The given expression can be simplified to = 3 * 97 * 57 * 40. So,the highest prime factor would be 97.

Last edited by subhendu009 on 04 Apr 2013, 05:56, edited 1 time in total.

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04 Apr 2013, 06:45

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Expert's post

Here is a question from my side.

A Train left Mumbai for Pune at noon sharp. Two hours later, another train started from Mumbai in the same direction. The second train passed the first one at 8 P.M. Find the average speed of the two trains over the journey if the sum of their average speeds is 70 kmph

a) 28.50 kmph b) 30 kmph c) 34.26 kmph d) 35 kmph e) 55 kmph

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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02 Apr 2013, 13:28

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There is a crack at the bottom of a tank. Before the crack appeared, pipe A could fill the tank in 2 hours. Now it takes 30 min longer. How long will the crack take to empty a full tank when pipe A is closed ?

Shortcut : If the pipe can fill a tank in 'a' hours but takes 'x' hours longer due to a leak, then the time taken by the leak to empty the tank fully is \(a(1+a/x)\)

Or Before the crack appeared , Pipe A could fill \(1/2\) the tank in an hour. Now it takes 2 hours 30 mins to fill the tank. That is \(5/2\) hours. Hence, it fills \(2/5 th\) of the tank every hour. The crack at the bottom accounts for this reduction in the amount . The crack therefore drains \(1/2-2/5 =5-4/10 =1/10 th\)of the tank every hour Hence , total time taken to drain the tank is C)10 hours

Last edited by thinktank on 02 Apr 2013, 15:13, edited 1 time in total.

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04 Apr 2013, 07:05

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A and B together can do a work in 20 days. B and C together can finish it in 25 days. If A does double the work in a day than C, then the number of days in which C alone can finish it is?

A) 70 days B) 80 days C) 85 days D) 100 days E) 120 days

Solution :- Let the work be 100% A and B together can do a work in 20 days. that mean in a day they are doing 100/20 = 5 % of work B and C together can finish it in 25 days. that means in a day they are doing 100/25 = 4% of work B + A = 5 B + C = 4 A does double the work in a day than C. So A = 2C B + 2C = 5 B + C = 4 Upon Solving we get C = 1 that mean C does 1% of the work in a day, Hence to complete the whole work it would take him 100 days.

D A handy shortcut : When ever a trader marks his goods up by \(x%\) and offers a discount of \(y%\) then the profit/loss percentage he makes is given by \(x-y-(xy/100)\)

+1 if u think this approach would help you save precious time

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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06 Apr 2013, 06:48

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Here is one more : this time on Permutations and Combinations

Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. Find the total number of ways in which each of the five persons can leave the cabin i) At any one of the 7 floors ii) At different floors.

A) i) 7^5 ii) 7! B) i) 35 ii) 7! C) i) 5^7 ii) 7! D) i) 5^7 ii) 2520 E) i) 7^5 ii) 2520

Correct Choice is E Let the five persons be b,c,d,e,f I) b can leave the cabin at any one of the seven floors. So he has 7 options Similarly each of c,d,e,f also has 7 options. Thus the total number of ways in which each of the five persons can leave the cabin at any of the seven floors is 7 X 7 X 7 X 7 X7 = 7^5 II) b can leave the cabin in 7 ways. c can leave the cabin in 6 ways, since he can not leave at where b left. In the same way d has 5, e has 4, and f has 3 way. Hence total number of ways = 7 X 6 X 5 X 4 X 3 = 2520

the sequence is as follow: \(a_1=-81\) \(a_2=-78\) ... and this will reach 0 is 27 passages \(a_{28}=0\) and then will become positive and every term will balance its negative correspondent.

\(a_{27}=-3\) will be balanced by \(a_{29}=3\) => sum=0 and so on... This process continues for all terms, if the question were "What is the sum of the first 55 terms the balance will be perfect and the sum would be 0.

But here we are asked the sum of the 54 terms: the very first term will not be balanced! \(a_{1}=-81\), \(a_{2}=-78\), ..., \(a_{54}=78\)

The sum is -81.

Given \(a_1=-81\) , and \(a_n=a_{n-1}+3\) for \(n>1\),

Therefore, \(a_2=a_{1}+3\) & \(a_3=a_{2}+3\)

This means the Common increment of 3, & as we know that there are 54 terms in total but if we remove \(a_1\) , then we will have 53 terms each increasing with the common increment of 3. Therefore we have \(a_54\) as 3*53-81.

\(a_54\) =159 - 81 \(\Rightarrow\) \(a_54\) =78.

Now, we have first term & the last term & the common difference. so as per the properties.....

--> \(\frac{Last Term + First Term}{2} * Total # of Terms\)

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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04 May 2013, 23:49

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Question :

Two cars move along a circular track 1.2 miles long at constant speeds. When they move in opposite directions, they meet every 15 seconds. However, when they move in same direction, once car overtakes the other car every 60 seconds. What is the speed of the faster car ?

Options :

A) 0.02 miles/s B) 0.03 miles/s C) 0.05 miles/s D) 0.08 miles/s E) 0.1 miles/s

- Let the speed of the 2 dots be "a" (faster dot) and "b" (slower dot) miles/s respectively. - When they move in opposite directions, \(\frac{1.2}{a+b}=15\) - When they move in same direction, \(\frac{1.2}{a-b}=60\) - Simplifying 2 equations, we get 15a + 15b = 1.2 and 60a - 60b = 1.2 - Solving 2 equations, 120a = 6 or a = 0.05 miles/s

_________________

Kudos Please... If my post helped.

Last edited by dipen01 on 05 May 2013, 00:03, edited 1 time in total.

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17 May 2013, 22:05

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My .02 cents

The Oxford press compiled a 2000 page dictionary but just before printing,it was found that page numbers are missing. How many times should typist press keys from 0-9 so as to number dictionary from 1-2000?

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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01 Apr 2013, 21:07

vandygrad11 wrote:

Great idea. This is probably a great way to ingrain things for question writers. My Quant strength is exponents, so I'll get things started with one of those:

If \(\frac{4^{3x}}{16^{3x/2}} = (2)(2^{-3x})\), what is x?

A) x = 1/3 B) x = 2/3 C) x = 1 D) x = 3/2 E) x = 3

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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02 Apr 2013, 14:56

Expert's post

thinktank wrote:

There is a crack at the bottom of a tank. Before the crack appeared, pipe A could fill the tank in 2 hours. Now it takes 30 min longer. How long will the crack take to empty a full tank when pipe A is closed ?

A)15 hours

B)8 hours

C)10 hours

D)12 hours

E)15 hours

I'm not aware as to how to post the Answer under REVEAL here.. can someone edit this post plz ? Solution :

Shortcut : If the pipe can fill a tank in 'a' hours but takes 'x' hours longer due to a leak, then the time taken by the leak to empty the tank fully is \(a(1+a/x)\)

Or Before the crack appeared , Pipe A could fill \(1/2\) the tank in an hour. Now it takes 2 hours 30 mins to fill the tank. That is \(5/2\) hours. Hence, it fills \(2/5 th\) of the tank every hour. The crack at the bottom accounts for this reduction in the amount . The crack therefore drains \(1/2-2/5 =5-4/10 =1/10 th\)of the tank every hour Hence , total time taken to drain the tank is C)10 hours

Done. Mark the text you want to hide and press "Spoiler" button. _________________

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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02 Apr 2013, 15:13

Here is the one from my side:

DS

If x and y are positive, is \(2x^2/17+y^2/4 < 1\)? (1) \(2y>x^2\)

(2) \(x^2 < 9-y^2\)

1.Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. 2.Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 3.BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 4.EACH statement ALONE is sufficient. 5.Statements (1) and (2) TOGETHER are NOT sufficient.

Ans. 2 This can be solved graphically. The equation in the question stem is the equation of an ellipse with x-intercept ~ 3 and y-intercept 2 and represents the area inside the ellipse. The statement 1 is the equation of the area enclosed inside a parabola and only some of the enclosed area will intersect with the enclosed area of ellipse. NOT SUFFICIENT. The statement 2 is the equation of the enclosed area of a circle with radius 3 and will therefore completely enclose ellipse as x-intercept of ellipse < 3 and y-intercept of ellipse is also less than 3. SUFFICIENT.

Re: Submit Your Own GMAT Math Questions - Get GMAT Club Tests [#permalink]

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03 Apr 2013, 21:07

vandygrad11 wrote:

vandygrad11 wrote:

Great idea. This is probably a great way to ingrain things for question writers. My Quant strength is exponents, so I'll get things started with one of those:

If \(\frac{4^{3x}}{16^{3x/2}} = (2)(2^{-3x})\), what is x?

A) x = 1/3 B) x = 2/3 C) x = 1 D) x = 3/2 E) x = 3

Kudos for the question but just looking at it first time I thought of a easier way. Correct me if i am wrong

\(\frac{4^{3x}}{16^{3x/2}} = (2)(2^{-3x})\) \(\frac{(4)^{3x}}{(4)^{2*3x/2}} = 2^{1-3x}\) Numerator and denominator are equal after cancelling out the 2 \(1 = 2^{1-3x}\)

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