1. If N and Y are positive integers and 450y=N^3, which of the following must be an integer?

1) y/(3 x 2^2 x 5) - > Correct

2) 7/(3^2 x 2 x 5)

3) y/(3 x 2 x 5^2)

N^3 = 450y = 3*3 * 5*5 * 2

Minimum value of Y 3*5*2*2

3. Is integer K divisible by 16?
1) 8k is divisible by 16
8k = 16a
k = 2a

Not Sufficient

2) 9k is divisible by 12
9k = 12b
3b = 4b

Not Sufficient

Statement 1 and 2 together
3k = 6a = 4b = 12c
k = 4c

Not Sufficient

Answer: E

4. A certain company has six senior officers and 4 junior officers. A committee is to be created of 3 seniors and 1 junior, how many different committees are possible?

6C3 * 4C1

2. If the speed of x m/s =y km/h, what is y in terms of x? (1 km = 1,000 meters)


1 km/hr = 5/18 m/s (1000m/60*60 s)

so y = 5/18*x m/s

Hope this helps

5. Alices pay was the same each month, and she saved the same fraction of her pay each month for a year. The total amount she saved at the end of the year was 3 times the amount of the portion she did not save. If all the money she saved was from her take home pay, what fraction did she save each month?

https://www.manhattangmat.com/forums/ali ... t3103.html
https://www.beatthegmat.com/alice-s-take ... 13865.html

Above all problems are from GMATprep. Solution of all the problems from GMATprep is available on forum. Please check before posting.

for question 3 - divisible by means to have all of the same factors as - so the question is asking whether k has all the same factors as 16 (or does k contain 4 2's)

1. stmt 1 says 8k is divisible by 16 which only tells you that k has one two as a factor - insufficient

2. 9k/12 tells you that k has 2 twos as factors (because after you take out the three contained in the 9 you are left with a denominator of 4- insufficient


Together they still only tell you that k has two 2s as factors and that is not enough.

WHy combination formula, i think here the order does not matter , thus 6p3 * 4p1 will be valid... comment

1. If N and Y are positive integers and 450y=N^3, which of the following must be an integer?

1) y/(3 x 2^2 x 5)

2) 7/(3^2 x 2 x 5)

3) y/(3 x 2 x 5^2)
[spoiler]
Ans - 450Y = 2*5*5*3*3 = N^3. For this equation to hold good 450 Y should be a cube and the minimum possible value of Y is 2*2*5*3 = 60. Only Option 1 satisfies this.
[/spoiler]

2. If the speed of x m/s =y km/h, what is y in terms of x? (1 km = 1,000 meters)
[spoiler]
Ans 1 km/hr = 5/18 m/s (1000m/60*60 s) hence y = 5/18*x m/s
[/spoiler]
3. Is integer K divisible by 16?
1) 8k is divisible by 16
2) 9k is divisible by 12
[spoiler]
Ans - 1 not sufficient as k can be 2,4,6,8...16,18...so on some of them will be divisible by 16 and some wont

2 - Not sufficient - reason similar to 1

1&2 together - K can be 4,8,12,16,20,24,28,32....so on some of them will be divisible by 16 and some wont.
Hence Ans will be (E)
[/spoiler]
4. A certain company has six senior officers and 4 junior officers. A committee is to be created of 3 seniors and 1 junior, how many different committees are possible?
[spoiler]
Ans - 6C3 * 4C1 = 80
[/spoiler][/spoiler]

5. Alices pay was the same each month, and she saved the same fraction of her pay each month for a year. The total amount she saved at the end of the year was 3 times the amount of the portion she did not save. If all the money she saved was from her take home pay, what fraction did she save each month?

Here's my approach:

portion saved = y

portion not saved = 1 - y

portion saved = 3*(portion not saved)

y = 3(1-y)

y = 3 - 3y

y = 3/4