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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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GMAT Prep Practice Test

by LizinCali » Tue Nov 18, 2008 9:53 pm
Thanks in advance for your help. I'm having trouble with following problems (mostly with set up):

At a certain college there were twice as many English majors as History majors and three times as many English majors as Math majors. What is the ratio of the number of History majors to the number of Math major?

6 to 1
3 to 2
2 to 3
1 to 5
1 to 6

38, 69, 22, 73, 31, 47, 13, 82
Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

56
68
69
71
73

A used car dealer sold one car at a profit of 25% of the dealer's purchase price for that car and sold another car at a loss of 20% of the dealer's purchase price for that car. If the dealer sold each car for $20,000, what was the dealer's total profit or loss, in dollars, for the two transactions combined?

$1000 profit (this was my answer!)
$2000 profit
$1000 loss
$2000 loss
$3334 loss

A retailer sold an appliance for $80. If the retailer's gross profit on the appliance was 25% of the retailer's cost for the appliance, how many dollars was the retailer's profit?

(i keep coming up with $15!)
$10
$16
$20
$24
$25

What was Jean's insurance premium in 1995?
1) The ratio of Jean's insurance premium in 1995 to her insurance premium in 1994 was 6/5
2) Jean's insurance premium in 1995 was 20% more than her premium in 1994

On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5/2. What was the number of men on the sight-seeing tour?
1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5/11
2) The number of women on the sight-seeing tour was less than 30


Thank you!

LizinCali :? :oops:
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by LizinCali » Tue Nov 18, 2008 10:03 pm
Fogot to list answers...

1) 3 to 2
2) 71
3) [spoiler]$1000 loss[/spoiler]
3) [spoiler]$16[/spoiler]
4) E
5) C


Thanks again!

LizinCali
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by aditi_bc » Wed Nov 19, 2008 12:02 am
1) When you see multiple ratios which are related by a common element(in this case English Major), try to multiply the ratios to make the common element same number.

So multiply E:H=2:1 by 3 => E:H=6:3
& E:M=3:1 BY 2 => E:M=6:2

Thus, H:M=3:2

2) Not sure about the wording of the question but here is what I think it means.
Solution:Arrange the no.s in ascending order
13,22,31,38,47,69,73,82

Total numbers n=8

3/4*8=6 i.e 6th number is 69 so the answer needs to be greater than 69
1/4*8=2 so the answer needs to be less than 73

Ans is 71

3) Let PP1 be the purchase price of first car, sold for $20,000 at 25% profit.
So, (1.25)PP1=20,000 [ as you know that 25% profit is 100+25=125% of cost price)

Similarly (0.80)PP2=20,000 (as 20% loss is 100-20=80% of cost price)

Solving for PP1& PP2
PP1=$16,000 So profit from 1st car=20,000-16,000=$4000

PP2=$25,000, So loss from 2nd car=25,000-20,000=$5000

Thus net loss of $1000

4) SP=$80, P=25% Thus 1.25CP=80 => CP=$64
P=SP-CP=80-64=$16

Ans is $16
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by Sreema » Thu Nov 20, 2008 11:50 am
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5/2. What was the number of men on the sight-seeing tour?
1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5/11
2) The number of women on the sight-seeing tour was less than 30

Ans:
from 1:
W : C = 5:2
C : M = 5:11
taking common ratio,
W:C:M = 25:10:22
from 2:

W<30 => W can be 25 =>M= 22

Ans = C
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by Carloblacksun » Thu Nov 20, 2008 2:41 pm
the key for the last problem, which might confuse somebody, is that PEOPLE are compared to INTEGERS...in theory, with less than 30 women, you might think to 5 children, 11 men and...12,5 women! which is impossible...clearly, women must be 25...

regarding the car dealer, this is quite simple...

$ 20000 with 25% margin...20000 * 100 / 125 = 16000 $ (cost of first car)
$ 20000 with 20% loss... 20000 * 100 / 80 = 25000 $ (cost of second car...

total Sales 40000 vs. total cost 41000 $ = loss of 1000!
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Confused

by vladmire » Thu Dec 04, 2008 7:38 pm
Can someone else this one again how is 73 the second number in ascending order?? should it now be 22 in the second and 69 is the sixth??

38, 69, 22, 73, 31, 47, 13, 82
Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

56
68
69
71
73
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by reneerenee » Fri Dec 05, 2008 11:07 am
if the ordering part is confusing to you, look at answer D, 71. 71 is less that 73 and 82. it's less than 2 out of the 8 numbers in the list, so it's less thatn 1/4.

71 is greater thatn the 6 of the numbers inthe list. 6 out of 8 is 3/4.
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by vish150783 » Mon Dec 08, 2008 5:37 am
aditi_bc wrote:1) When you see multiple ratios which are related by a common element(in this case English Major), try to multiply the ratios to make the common element same number.

So multiply E:H=2:1 by 3 => E:H=6:3
& E:M=3:1 BY 2 => E:M=6:2

Thus, H:M=3:2

2) Not sure about the wording of the question but here is what I think it means.
Solution:Arrange the no.s in ascending order
13,22,31,38,47,69,73,82

Total numbers n=8

3/4*8=6 i.e 6th number is 69 so the answer needs to be greater than 69
1/4*8=2 so the answer needs to be less than 73

Ans is 71

3) Let PP1 be the purchase price of first car, sold for $20,000 at 25% profit.
So, (1.25)PP1=20,000 [ as you know that 25% profit is 100+25=125% of cost price)

Similarly (0.80)PP2=20,000 (as 20% loss is 100-20=80% of cost price)

Solving for PP1& PP2
PP1=$16,000 So profit from 1st car=20,000-16,000=$4000

PP2=$25,000, So loss from 2nd car=25,000-20,000=$5000

Thus net loss of $1000

4) SP=$80, P=25% Thus 1.25CP=80 => CP=$64
P=SP-CP=80-64=$16

Ans is $16
I agree the second question looks ambiguous. It's not the regular GMAT type question.
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by mmslf75 » Sat Dec 26, 2009 5:11 am
aditi_bc wrote:1) When you see multiple ratios which are related by a common element(in this case English Major), try to multiply the ratios to make the common element same number.

So multiply E:H=2:1 by 3 => E:H=6:3
& E:M=3:1 BY 2 => E:M=6:2

Thus, H:M=3:2

2) Not sure about the wording of the question but here is what I think it means.
Solution:Arrange the no.s in ascending order
13,22,31,38,47,69,73,82

Total numbers n=8

3/4*8=6 i.e 6th number is 69 so the answer needs to be greater than 69
1/4*8=2 so the answer needs to be less than 73

Ans is 71

3) Let PP1 be the purchase price of first car, sold for $20,000 at 25% profit.
So, (1.25)PP1=20,000 [ as you know that 25% profit is 100+25=125% of cost price)

Similarly (0.80)PP2=20,000 (as 20% loss is 100-20=80% of cost price)

Solving for PP1& PP2
PP1=$16,000 So profit from 1st car=20,000-16,000=$4000

PP2=$25,000, So loss from 2nd car=25,000-20,000=$5000

Thus net loss of $1000

4) SP=$80, P=25% Thus 1.25CP=80 => CP=$64
P=SP-CP=80-64=$16

Ans is $16
PERFECT!!
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