Integer K, Ratio, Probability

Expert replies

MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Sun Jun 19, 2011 3:29 pm

What are the fast ways to solve these problems?

Thanks

1)
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?

2
5
10
15
65

2)

If 3/4 of the number of women working at Company X is equal to 2/3 of the number of men, what fraction of the employees at Company X are women?

5/12
8/17
1/2
7/12
8/9

3)

A coin is flipped 5 times.

Which is bigger?

A) Probability of getting 2 heads
B) Probability of getting 3 heads

Source: Beat The GMAT — Problem Solving | Sun Jun 19, 2011 3:29 pm

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sun Jun 19, 2011 9:35 pm

Hi,
Q1) 1040 = 13*8*10 = 13*5*16 = 65*4^2. So, to make it perfect square multiply by 65.

Q2) 3w/4 = 2m/3 => m = 9w/8
So, w/(m+w) = w/(9w/8 +w) = 8/17

Q3)p(H)=p(T) = 1/2
So, if a coin is flipped 5 times, p(2heads) = p(3tails) = p(3heads) as head and tail are equally likely.

Cheers!

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Jun 19, 2011 9:41 pm

Q1. If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?

2
5
10
15
65

Solution.

1040 = 2^4 * 5 * 13
Now for 1040k to be the square of an integer, k should be 5 * 13 = 65

The correct answer is E.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Jun 19, 2011 9:48 pm

Q2. If 3/4 of the number of women working at Company X is equal to 2/3 of the number of men, what fraction of the employees at Company X are women?

5/12
8/17
1/2
7/12
8/9

Solution.

Let the no. of women employees = W and no. of men employees = M
Then total no. of employees = W + M. We have to find the value of W/(W + M)
Then, 3W/4 = 2M/3 implies W = 8M/9
W/(W + M) = 8M/9 /(8M/9 + M) = 8M/9 * 9/17M = 8/17

The correct answer is B.

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Sun Jun 19, 2011 10:10 pm

1 1040 = 2^4 * 5 * 13.
thus k = 13*5 = 65.

3 1/2^5( 5c2) and 1/2^5(5c3). both give the same result.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Dec 19, 2017 6:59 am

If 3/4 of the number of women working at Company X is equal to 2/3 of the number of men, what fraction of the employees at Company X are women?

A) 5/12
B) 8/17
C) 1/2
D) 7/12
E) 8/9

We can let m = the number of men and w = the number of women. We need to determine the value of w/(w + m). We are given that:

(3/4)w = (2/3)m

w = (2/3)m x (4/3)

w = 8m/9

9w = 8m

We need to determine w/(w + m). Let’s multiply the numerator and the denominator by 8:

w/(w + m) = 8w/(8w + 8m) = 8w/(8w + 9w) = 8w/17w = 8/17

Answer: B

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Head of GMAT Instruction
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