Five Problems that I could use some quick help on. I take the test Saturday, wish me luck!
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)
2. If the speed of x m/s =y km/h, what is y in terms of x? (1 km = 1,000 meters)
3. Is integer K divisible by 16?
1) 8k is divisible by 16
2) 9k is divisible by 12
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?
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?
Five Problems that I could use some quick help on. Thanks!
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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
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
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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
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
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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.
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.
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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.
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.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA
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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]
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
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