gmat prep1 q's. please help!

[karenmeow]

please help me with these questions... i dont know how to get the answer!

1. pump a, b, & c operate at constant rates. pump a & b, simultaneously, fill a tank in 6/5 hr; pump a & c, simultaneously, fill a tank in 3/2 hr; pump b & c, simultaneously, fill a tank in 2 hrs. how many hrs does it take a, b, & c, simultaneously, to fill a tank?

answer: 1 hr

2. if each term in sum a1+a2+...+an is either 7 or 77, and the sum equals 350, which can be n?
choices: 38, 39, 40, 41, 42

answer: 40

3. alice's take home pay is the same each month. she saves same fraction each month. the total amt she saved at the end of the year was 3 times the amt of the portion she did NOT save. if all the money she saved last yr was from her pay, what fraction of her pay did she save each month?

answer: 1/5

4. the perimeter of an isosceles right triangle is 16+16(sq rt 2). what is the length of the hypotenuse?

answer: 16

5. 3 grades of milk are 1%, 2%, 3% fat. if x gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x+y+z gallons a 1.5% grade, what is x in terms of y & z?

answer: y+3z


thanks!

[lunarpower]

please post problems in separate threads.

i have performed this separation for these problems as a courtesy (to you and, more importantly, to the thousands of other users who prefer 1 problem per post); if you post problems in the future, please create a separate thread for each problem.
thank you.

the first problem may be found at
https://www.beatthegmat.com/pump-a-b-c-o ... html#57014

[lunarpower]

third problem
https://www.beatthegmat.com/alice-s-take ... html#57071

[lunarpower]

second problem
https://www.beatthegmat.com/if-each-term ... 13856.html

[lunarpower]

4th problem (from another forum)

https://www.manhattangmat.com/forums/iso ... t2694.html

[antyagi]

In the 3rd problem, where does the problem states that the
"the total amt she saved at the end of the year was 3 times the amt of the portion she did NOT save" is applicable for a year.
i.e instead of 12x = 3(x-y) why it cannot be x = 3(x-y) ??

[vivekverma]

Solutions :

1. 1/a+1/b = 5/6
1/a+1/c = 2/3
1/b+1/c = 1/2

2(1/a+1/b+1/c)=5/6+2/3+1/2
=> 1/a+1/b+1/c = 1

2. Out of n numbers, let no. of 77's be x :
So, we have sum = 77x + 7(n-x) = 350
=> n+10x = 50
For different values of x : if x=1 n=40(Ans.)

3. For isosceles triangle, sides = x,x,x(root 2)
Sum of all sides = perimeter = 2x+x(root 2) = 16+16(root 2)
=> 16(1+root2) = (root2)x(1+root2)
=> x(root 2) = 16 (Ans.)

4. Total Pay = P
Saving = S
12 month saving = 12*S = 3(P-S)
=> S/P = 1/5

[hakyology]

0.01x + 0.02y + 0.03z = 0.015(x + y + z )

then u will get y+3z.

[lunarpower]

In the 3rd problem, where does the problem states that the
"the total amt she saved at the end of the year was 3 times the amt of the portion she did NOT save" is applicable for a year.
i.e instead of 12x = 3(x-y) why it cannot be x = 3(x-y) ??

the original poster left out the rather important word "monthly" in the original problem statement.

go to the separate thread i created for that problem; i've posted the correction there.