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Please Help: Math Questions from GMATPrep that I can't solve

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Manager
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Joined: 13 Mar 2007
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Please Help: Math Questions from GMATPrep that I can't solve [#permalink] New post 13 Jun 2007, 13:30
If you know how to solve these, please let me know. Thanks!

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1) 70, 75, 80, 90, 105, 105, 105, 130, 130, 130.
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

a) One
b)Two
c)Three
d)Four
e)Five



------------------------------------------------------------------------------------
2) The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions?(1 kilogram = 1000 gram and 1 cubic meter = 1,000,000 cubic centimeters)

a)0.80
b)1.25
c)8.00
d)12.50
e)80.00



-----------------------------------------------------------------------------------
3)Equal amounts of water were poured into two empty jars of different capacities, which made one jar 1/4 full and other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water?

a)1/7
b)2/7
c)1/2
d)7/12
e)2/3

----------------------------------------------------------------------------------------

4)A certain candy manufacturer reduced the weight of Candy Bar M by 20 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?

a)5%
b)10
c)15%
d)20%
e)25%


---------------------------------------------------------------------------------------
5) A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

a)5
b)4
c)3
d)2
e)1


---------------------------------------------------------------------------------------
6)Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had

a)a profit of $10
b)a profit of $8
c)a loss of $8
d)a loss of $10
e)neither a profit nor a loss


-------------------------------------------------------------------------------------------
7)A certain store found that last year the average(arithmetic mean) monthly sales from January through October was $120,000. In November and December, the monthly sales were 3 and 5 times, respectively, the average for the other 10 months. What was the store's average monthly sales last year?

a)$180,000
b)$216,000
c)$252,000
d)$318,000
e)$360,000

----------------------------------------------------------------------------------------

8)Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time, in hours, that machine B must operate?

a)4
b)4 2/3
c)5 1/3
d)6
e)6 1/4
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 [#permalink] New post 13 Jun 2007, 13:51
Quote:
3)Equal amounts of water were poured into two empty jars of different capacities, which made one jar 1/4 full and other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water?

a)1/7
b)2/7
c)1/2
d)7/12
e)2/3


The answer is C. imagine 2 jars: A and B. 1/4A = 1/3B b/c the same amount of water is in each 1/4 + 1/3B will equal 1/2A. remember 1/3B = 1/4A. make sense?

Quote:
4)A certain candy manufacturer reduced the weight of Candy Bar M by 20 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?

a)5%
b)10
c)15%
d)20%
e)25%


I picked #s and got E:
5 oz bar = $1.00. a 20% reduction in weight amts. to 4 oz
4 oz bar = $1.00

5 oz bar was .20 per ounce and the 4 oz bar is .25 per ounce.
difference/original * 100 = % change
5 = (.25 - .20)/.20 * 100 = 25%

Quote:
5) A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

a)5
b)4
c)3
d)2
e)1


I drew this out and got 3.
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Joined: 12 Jun 2006
Posts: 537
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 [#permalink] New post 13 Jun 2007, 14:17
Quote:
6)Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had

a)a profit of $10
b)a profit of $8
c)a loss of $8
d)a loss of $10
e)neither a profit nor a loss


I get E. 96*1.2 = 115.20 and 96*.8 = 76.8. he paid 115.20 for 1 and 76.8 for the other. 115.2 + 76.8 = 192. he sold each stock for $96. $96*2 = 192. neither p nor l. i think you can reason this one out too. 20% above and 20% under should cancel one another out.

Quote:
7)A certain store found that last year the average(arithmetic mean) monthly sales from January through October was $120,000. In November and December, the monthly sales were 3 and 5 times, respectively, the average for the other 10 months. What was the store's average monthly sales last year?

a)$180,000
b)$216,000
c)$252,000
d)$318,000
e)$360,000


I get A.

avg. = total/# of terms, 120K = total/10, total = 120K*10 = 1.2M
1.2M + 360K + 600K = 2.16 M, 2.16M/12 = 180K

Quote:
8)Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time, in hours, that machine B must operate?

a)4
b)4 2/3
c)5 1/3
d)6
e)6 1/4


Machine A can produce 72000 pencils in 8 hrs. that leaves 28K to be produced. Machine B can do that in 4hrs.

Quote:
1) 70, 75, 80, 90, 105, 105, 105, 130, 130, 130.
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

a) One
b)Two
c)Three
d)Four
e)Five


If I'm correct in my understanding of SD the answer is 2

the avg. of the 10 times is 102 seconds. 102 - 22.4 (sd) = 79.6. 70 and 75 are the only 2 numbers outside the below mean of the sd.
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Re: Please Help: Math Questions from GMATPrep that I can't s [#permalink] New post 13 Jun 2007, 19:31
1) 70, 75, 80, 90, 105, 105, 105, 130, 130, 130.
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

a) One
b)Two
c)Three
d)Four
e)Five

Average (AVG) = Sum/10 = 102
"More than 1 SD below 102" eq to "Below 102-22.4 = 79.6". Two of the running times fall in this description => B.


------------------------------------------------------------------------------------
2) The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions?(1 kilogram = 1000 gram and 1 cubic meter = 1,000,000 cubic centimeters)

a)0.80
b)1.25
c)8.00
d)12.50
e)80.00

100^3 cm3 ... 800 kg (=800,000 g) => 1,000,000 cm3/800,000 = 1.25cm3 per gram of the substance => B.


-----------------------------------------------------------------------------------
3)Equal amounts of water were poured into two empty jars of different capacities, which made one jar 1/4 full and other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water?

a)1/7
b)2/7
c)1/2
d)7/12
e)2/3

The jar w/ the larger capacity is the one which was less filled (1/4 of its total capacity) => if we pour the same amount in it, 1/2 of its total capacity will be filled => C.

----------------------------------------------------------------------------------------

4)A certain candy manufacturer reduced the weight of Candy Bar M by 20 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?

a)5%
b)10
c)15%
d)20%
e)25%

Initially: $/W.
Afterwards: $/0.8W = 1.25$/W => the increase in price per ounce was of 25% => E.


---------------------------------------------------------------------------------------
5) A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

a)5
b)4
c)3
d)2
e)1

To put each orange on exactly four oranges from the right-below-layer, the order of oranges should be:

OOOOO
OOOOO
OOOOO (1st layer)

OOOO
OOOO (2nd layer)

OOO (3rd layer) => C.


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6)Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had

a)a profit of $10
b)a profit of $8
c)a loss of $8
d)a loss of $10
e)neither a profit nor a loss

Initial price of share with which he profited: 96 = 1.2X => X = 80
Initial price of share with which he lost: 96 = 0.8Y => Y = 120

On both shares, the investment went from 80+120=200 to 96*2=192; that is, he lost 200-192=8$ => C.


-------------------------------------------------------------------------------------------
7)A certain store found that last year the average(arithmetic mean) monthly sales from January through October was $120,000. In November and December, the monthly sales were 3 and 5 times, respectively, the average for the other 10 months. What was the store's average monthly sales last year?

a)$180,000
b)$216,000
c)$252,000
d)$318,000
e)$360,000

Yearly sale = 120,000*10 + 120,000*(3+5) = 2,160,000
AVG sale per month = 2,160,000/12 = 180,000 => A.


----------------------------------------------------------------------------------------

8)Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time, in hours, that machine B must operate?

a)4
b)4 2/3
c)5 1/3
d)6
e)6 1/4

To find the least amount of time B will work, we need to assume A´ll work the most possible (8 hs) => A: 9000*8 = 72,000 pencils => B:100,000-72,000 = 28,000 (pencils to produce) => 28,000/7000 (per hr) = 4 hs will B operate => A.

[/quote]
Re: Please Help: Math Questions from GMATPrep that I can't s   [#permalink] 13 Jun 2007, 19:31
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