Data sufficiency problems

[dbajaj]

Hi,
Please help me these data sufficiency questions:
Question # 6
What is the sum of the integers k, l, m?
(I) The average of the three numbers is less than 21.
(II) The average of the three numbers is more than 19.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

(D) Each statement ALONE is sufficient

(E) Statements (1) and (2) TOGETHER are NOT sufficient

Your Answer 5
Actual Answer 3

The actual answer does not hold when we consider 17,20 & 22 as the three numbers....In this case, the average is 19.67,which is valid since nowhere in the question it is stated that the average should be an integer. Had this been the case then it would ahve been possible to get to answer 3.
--- Question # 3
Tshui is 3 years older than Tshang. What is the sum of their present ages?
(I) The ratio of their present ages is 4 : 3.
(II) After 6 years the ratio of their ages will be 5 : 6.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

(D) Each statement ALONE is sufficient

(E) Statements (1) and (2) TOGETHER are NOT sufficient

Your Answer 1
Actual Answer 4

In this case, solving choice 2 yields a negative answer for the age.....



LadyD

[isha]

Question # 6
What is the sum of the integers k, l, m?
(I) The average of the three numbers is less than 21.
(II) The average of the three numbers is more than 19.

I think the correct answer is 5

--- Question # 3
Tshui is 3 years older than Tshang. What is the sum of their present ages?
(I) The ratio of their present ages is 4 : 3.
(II) After 6 years the ratio of their ages will be 5 : 6.

correct answer is 4

Consider the age of Tshang as x, Tshui is x+3
after six years their ages will be x+6 and x+9

x+6/x+9 = 5/6

6x +36 = 5x+45
x = 9
which is fine

[dbajaj]

Thanks Isha for your reply.

Please have a look at the following questions:

1. If q is a multiple of prime numbers r, is q a multiple of r?
1. r<4
2. q=18.

My answer b.
correct answer e

2. It takes 16 days for 48 women to complete a job that requires 16 men to complete in 24 days. 12 men initiated the work and after 14 days, 12 women joined them.How many days will they together take to complete the job.

ans. 12 days.


Thanks,
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LadyD

[raghuveer_v]

2. It takes 16 days for 48 women to complete a job that requires 16 men to complete in 24 days. 12 men initiated the work and after 14 days, 12 women joined them.How many days will they together take to complete the job.

ans. 12 days

Consider the entire job as one unit : 1

Work(fraction of the entire job) done by 1 woman in 1 day (w)

w = 1 / (16 x 48)

Work done by 1 man in 1 day (m)

m = 1 / (16 x 24) = 2w

Work done by 12 men in 14 days (a)

a = 12 x 14 x m = 12 x 14 x 2w

Remaining job : b = 1 - a

After 12 women join, let them complete the remaining job in n days


job done by 12 men + 12 women in 1 day = 12 w + 12 m = 36 w

job done by 12 men + 12 women in n days (b)

b = n x ( 12 m + 12 w ) = n x 36w

We know,

b = 1-a

n x 36 w = 1 - 12 x 14 x 2w

n x 36 / (16 x 48) = 1 - [12 x 14 x 2 / (16 x 48)]

n = [(16 x 48) - (12 x 14 x 2)] / 36

n = 432 / 36 = 12 days

So, they together take 12 days to complete the job


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[tasimota]

ooh, that is rather technical Raghuveer. Try using proportions. The job is being done by 3/4 the original number of men. So the job will take 4/3 as long as original. 4/3 of 24 is 32, of which 14 is done, leaving us with 18 days of work for the men.

The last thing is to realize that the women are half as fast from the men, which you get from the beginning. So adding 12 women is like adding 6 men to the 12 doing the job, so now we have 18. This is 50% more (or 3/2 as much) so the job will be completed in 2/3 the time. 2/3 of 18 is.....

12, with the men and women working together.

Sincerely,

[raghuveer_v]

Originally posted by tasimota

ooh, that is rather technical Raghuveer. Try using proportions. The job is being done by 3/4 the original number of men. So the job will take 4/3 as long as original. 4/3 of 24 is 32, of which 14 is done, leaving us with 18 days of work for the men.

The last thing is to realize that the women are half as fast from the men, which you get from the beginning. So adding 12 women is like adding 6 men to the 12 doing the job, so now we have 18. This is 50% more (or 3/2 as much) so the job will be completed in 2/3 the time. 2/3 of 18 is.....

12, with the men and women working together.

Sincerely,

Know what, when I looked at my own post (after 6 months, though), I was thinking...."what a mess! does one really need to do all this to get the answer?"

I couldn't go through all my workin, and then yours...

You are most probably right. What an elegant solution!

Sincerely,