Data Sufficiency

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

1) the ratio of children to men was 5 to 11.
2) the number of women was less than 30.

IMO E

sbasha wrote:IMO E

NOT E

IMO C

Question Stem:
W:C = 5:2

Stmt1 :

C:M = 5:11

Insufficient

Stmt 2:

Number of Women < 30

Insufficient

Stmt 1 and Stmt 2:

W:C:M = 25:10:22
Number of women is 25x < 30
=> x < 30/25
=> x < 6/5
=> x < 1.2

In this stem, i think we should consider the common factor an integer, coz for any real number, the number of women, children, and men will be a fraction, which is logically not possible.

Hence x < 1.2 yeilds x = 1.

Hence total number of men = 22 * 1 = 22

Sufficient

Note: x cannot be -ve either, since we are dealing with a quantity.

Hence IMO C

pradeepsarathy wrote:Question Stem:
W:C = 5:2

Stmt1 :

C:M = 5:11

Insufficient

Stmt 2:

Number of Women < 30

Insufficient

Stmt 1 and Stmt 2:

W:C:M = 25:10:22
Number of women is 25x < 30
=> x < 30/25
=> x < 6/5
=> x < 1.2

In this stem, i think we should consider the common factor an integer, coz for any real number, the number of women, children, and men will be a fraction, which is logically not possible.

Hence x < 1.2 yeilds x = 1.

Note: x cannot be -ve either, since we are dealing with a quantity.

Hence IMO C

What do you represent by X?. How did you get 25:10:22 ???

When we are dealing with ratios, we are actually diving the quantity of two entities -

For ex - Ratio of number of women to children is 5:2 implies, the total number of women divided by total number of children resolves to the fraction 5/2.

Total No. of women can be - 5, 10, 15, 20, 25, 30 ....

Total No. of children can be - 2, 4, 6, 8, 10, 12, ....

Each pair,respectively resolves to the ratio 5:2 (Eg - 30/12 can be simplified to 5/2)

Hence whenever ratios are mentioned, the total number of that particular entity is assumed to be some multiple, generally 'x'.

So in this case total number of women is 5x and total number of children is 2x.


To answer the second part of the question -

We are give w:c = 5:2 and c:m = 5:11

The quantity 'c' is the common connector between 'w' and 'm'.In order to have common relationship among w,c and m, we need to make sure that 'm' and 'w' relate to same quantity of 'c'.

multiplying 'w' by 5 and 'c' by 5 gives us w:c = 25:10
similarly multiplying 'c' by 2 and 'm' by 2 gives us c:m = 10:22

Now we can relate all the three quantities, w:c:m = 25:10:22

According to this relation -

Total numebr of Women = 25x
Total number of Children = 10x
Total number of Men = 22X

Hope my explanation is clear.

pradeepsarathy wrote:When we are dealing with ratios, we are actually diving the quantity of two entities -

For ex - Ratio of number of women to children is 5:2 implies, the total number of women divided by total number of children resolves to the fraction 5/2.

Total No. of women can be - 5, 10, 15, 20, 25, 30 ....

Total No. of children can be - 2, 4, 6, 8, 10, 12, ....

Each pair,respectively resolves to the ratio 5:2 (Eg - 30/12 can be simplified to 5/2)

Hence whenever ratios are mentioned, the total number of that particular entity is assumed to be some multiple, generally 'x'.

So in this case total number of women is 5x and total number of children is 2x.


To answer the second part of the question -

We are give w:c = 5:2 and c:m = 5:11

The quantity 'c' is the common connector between 'w' and 'm'.In order to have common relationship among w,c and m, we need to make sure that 'm' and 'w' relate to same quantity of 'c'.

multiplying 'w' by 5 and 'c' by 5 gives us w:c = 25:10
similarly multiplying 'c' by 2 and 'm' by 2 gives us c:m = 10:22

Now we can relate all the three quantities, w:c:m = 25:10:22

According to this relation -

Total numebr of Women = 25x
Total number of Children = 10x
Total number of Men = 22X

Hope my explanation is clear.

Thank you so much for your explanation. I only miss how we will find the number of men from this:

In this stem, i think we should consider the common factor an integer, coz for any real number, the number of women, children, and men will be a fraction, which is logically not possible.

Hence x < 1.2 yeilds x = 1.

Note: x cannot be -ve either, since we are dealing with a quantity.

since the ratio is 25:10:22,
the total quantity is 25x, 10x, 22x respectively....
since we know the value of x, total number of men = 22 * x = 22 * 1 = 22.