Problem Solving

Could someone help me on this 4 questions??
tnks a lot


1 - On a certain sight seeing tour, the ratio of the number of women to the number of children was to 5 to 2. What was the number of the men on the sight seeing tour?

1) On the sight seeing tour, the ratio of the number of children to the number of men was 5 to 11
2) The number of women on the sight seeing tour was less than 30

Answer: C) Both statements together

2 – If n and y are positive integer and 450y = n^3, which must be an interger?
I. y/(3*(2^2)*5)

II. y/((3^2)*2*5)

III. y/(3*2*(5^2))

a)None
b)I only
c)II only
d)III only
e)I, II and III

Answer: B

3 – For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is:

a)between 2 and 10
b)between 10 and 20
c)between 20 and 30
d)between 30 and 40
e)greater than 40

Answer: E


4 – What fraction of this year’s graduating students at a certain college are males?

1)of this year’s graduating students, 33% of the males and 20% of the females transferred from another college
2)of this year’s graduating students, 25% transferred from another college

Answer : C) Both statements together

1 - On a certain sight seeing tour, the ratio of the number of women to the number of children was to 5 to 2. What was the number of the men on the sight seeing tour?

1) On the sight seeing tour, the ratio of the number of children to the number of men was 5 to 11
2) The number of women on the sight seeing tour was less than 30

Ans 1)

Ratio of W: C = 5:2

Statement 1) Ratio of M:C = 11:5

With Statement 1 and the info given in the stem you know the following-

1) You have to have a minimum of 5 children. Any less than 5 children the number of men in the group will not be an integer and since we are talking abt people u cant have a fraction.

2) But if u have 5 children the number of women in the group will be a fraction. So you need a minimum of 10 children in the group to satisfy the given ration. Now if u have 10 children the ratio of W:C:M will be 25:10:22

However since u are not given any more info u cannot come to the final ans. i.e total nos of men in the group. At this stage u only know the ratio

Statement 2) Says the nos of women in the group are less than 30. On its own its not enough info but together with statement 1 u can conclude the number of women has to be 25 so no. of men wil be 22

2 – If n and y are positive integer and 450y = n^3, which must be an interger?
I. y/(3*(2^2)*5)

II. y/((3^2)*2*5)

III. y/(3*2*(5^2))

a)None
b)I only
c)II only
d)III only
e)I, II and III

Ans 2)

Given Y and N are positive integer and 450y = n^3

450 = 3*3*5*5*2

Since 450 * Y is a cube of an integer Y has to be more than or equal to 3*5*2*2 (as 450 misses these numbers to make a perfect cube)

So ans is I only

3 – For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is:

a)between 2 and 10
b)between 10 and 20
c)between 20 and 30
d)between 30 and 40
e)greater than 40

Ans 3

This one is discussed in detail on the forum. Here is the link
https://www.beatthegmat.com/viewtopic.ph ... =100#24081


4 – What fraction of this year’s graduating students at a certain college are males?

1)of this year’s graduating students, 33% of the males and 20% of the females transferred from another college
2)of this year’s graduating students, 25% transferred from another college

Ans

Statement 1) 0.33M +0.2F are transferred
Statement 2) 0.25 (M+F) are transferred
Together we get 0.33M +0.2F = 0.25 (M+F)
Solving this equation we get M=5/8 F
So fraction of Males to total students is (5/8)F / ((5/8)F +F) = 5/13

thnks a lot for your help... very useful