problems from GMAT disclosed edition 55

Question

I'm not sure how to set up equations for these three problems. I managed to solve two of them through backsolving.

Can you help, pls?

1) If x dollars is invested at 10% for one year and y dollars is invested at 8% for one year, the annual income from the 10% investment will exceed the annual income from the 8% investment by $56. If $2,000 is the total amount invested, how much is invested at 8%?

a. $280
b. $800
c. $892
d. $1,108
e. $1,200

OA is B

2) The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed, in miles per hour?

a. 20
b. 30
c. 40
d. 50
e. 80

OA is C

It's obvious that r*t=d should be used here but not knowing rate or time for at least one car slightly confused me.

3) In a sample of college students, 40% are third-year students and 70% are not second-year students. What fraction of those students who are not third-year students are second-year students?

a. 3/4
b. 2/3
c. 4/7
d. 1/2
e. 3/7

OA is D

I tried to set up a grid for this with 3rd year, not 3rd year, 2nd year and not 2nd year entries but perhaps got it wrong.

thanks

gmat740 · Answer

2) The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed, in miles per hour?

a. 20
b. 30
c. 40
d. 50
e. 80

OA is C

For B =>
Speed=V
time=t

For A
Speed = v+10
time = t-2

Now distance = 400 = speed*distance
thus,

v*t = (v+10)*(t-2)

v= 5t-10

also v*t=400
so, (5t-10)*t = 400

t^2 - 2t -80 =0
t=10

so
v*t =v*10 =400

v=40

Hope this helps

gmat740 · Answer

3) In a sample of college students, 40% are third-year students and 70% are not second-year students. What fraction of those students who are not third-year students are second-year students?

a. 3/4
b. 2/3
c. 4/7
d. 1/2
e. 3/7

OA is D

I also did by grid method

Year Yes No
3rd 40 60
2nd 30 70

Ratio of the bold parts is the answer.(the question clearly says fraction)

Hope this helps[/list]

dtweah · Answer

LevelOne wrote:I'm not sure how to set up equations for these three problems. I managed to solve two of them through backsolving.

Can you help, pls?

1) If x dollars is invested at 10% for one year and y dollars is invested at 8% for one year, the annual income from the 10% investment will exceed the annual income from the 8% investment by $56. If $2,000 is the total amount invested, how much is invested at 8%?

a. $280
b. $800
c. $892
d. $1,108
e. $1,200

OA is B

2) The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed, in miles per hour?

a. 20
b. 30
c. 40
d. 50
e. 80

OA is C

It's obvious that r*t=d should be used here but not knowing rate or time for at least one car slightly confused me.

3) In a sample of college students, 40% are third-year students and 70% are not second-year students. What fraction of those students who are not third-year students are second-year students?

a. 3/4
b. 2/3
c. 4/7
d. 1/2
e. 3/7

OA is D

I tried to set up a grid for this with 3rd year, not 3rd year, 2nd year and not 2nd year entries but perhaps got it wrong.

thanks

1)

10X-8Y=5600
X+ Y= 2000

2) 400/B -400/ (B+10) =2

3) Third =40
First +Third +Fouth =70
2nd =30
If Thrid is 40 then those not third is 60

30/60=1/2

shibal · Answer

for the first 2 get the answer and put them back in the question, i did both of them in less than a minute....

for #3 it says 40% is 3rd grade and 70% are not 2nd grade, therefore 30% are 2nd grade. we have 40%+30%=70% the other 30% u can consider as others....

not 3rd year: 2nd+other 60%
2nd year: 30%

30/60 = 1/2

LevelOne · Answer

thanks, gmat740, can you explain how you got from v*t = (v+10)*(t-2) to v= 5t-10, pls? I'm not getting the same result.

gmat740 · Answer

thanks, gmat740, can you explain how you got from v*t = (v+10)*(t-2) to v= 5t-10, pls? I'm not getting the same result

v*t = v*t + 10t - 2v - 20
cancel v*t from both sides

thus, 10t-2v-20=0

2v = 10t-20
v = 5t-10(divide by 2)

Now I think,its quiet clear

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