A can complete a piece of work in 4 days. B takes double the time take

Question

A can complete a piece of work in 4 days: A = 1 work = 4 days

=> B = same work = 8 days

=> C = same work = 16 days

=> D = same work = 32 days

One pair = \(\frac{2}{3}\) [another pair]

=> A + D = 4 + 32 = 36 and B + C = 8 + 16 = 24

A + D = 36 * \(\frac{2 }{ 3}\) = 24 [B + C]

Answer D

(A) A, B 
(B) A, C 
(C) B, C 
(D) A, D
(E) C, D

CrackverbalGMAT · Accepted Answer

We can use the method of units of work.

Let the units of work done by each in their respective time periods = LCM(4,8,16,32) = 32 Units

Units of work done by A in 1 day =  \frac{32}{4}  = 8 units

Units of work done by B in 1 day =  \frac{32}{8}  = 4 units

Units of work done by C in 1 day =  \frac{32}{16}  = 2 units

Units of work done by D in 1 day =  \frac{32}{32}  = 1 units

\frac{Work \space done \space by \space slower \space pair}{Work \space done \space by \space faster \space pair} = \frac{2}{3}

A quick look tells us that =  \frac{6}{9}  =  \frac{2}{3}

does 8 + 1 = 9 units of work and   does 4 + 1 = 6 units of work

Therefore   takes  \frac{2}{3}  of the time of   (Since Work and Time are inversely proportional)

Option D

Arun Kumar

rajatchopra1994 · Answer

Explanation:

No.of days to complete work by A = 4 days
No.of days to complete work by B = 8 days
No.of days to complete work by C = 16 days
No.of days to complete work by D = 32 days
 
Since the first pair works fast, let us assume the first pair is A and B
 
Work can be completed by A and B in one day = (1/4) + (1/8) = 3/8
Number of days taken to complete the work by A and B = 8/3 days ...............(1)
 
Work can be completed by C and D in one day = (1/16) + (1/32) = 3/32
Number of days taken to complete the work by C and D = 32/3 days ...............(2)
 if we divide (1) by (2), we get ratio = 1/4. Hence the first pair is not A and B
 
similarly, if we make A and C as the first pair and try to find the ratio. The ratio can be worked out as 1/2.
Hence A and C are not in the first pair
 
let us try to make A and D as the first pair
 
Work can be completed by A and D in one day = (1/4) + (1/32) = 9/32
Number of days taken to complete the work by pair A and D = 32/9 days ...............(3)
 
Work can be completed by B and C in one day = (1/8) + (1/16) = 3/16
Number of days taken to complete the work by B and C = 16/3 days ...............(4)
 
if we divide (3) by (4), we get ratio = 2/3. Hence the first pair is A and D.

IMO-D

EgmatQuantExpert · Answer

Given

• A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task.

To Find

• They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work.

Approach and Working Out

• Time ratio - 
 o A : B : C : D = 1 : 2 : 4 : 8 
• Speed ratio – 
 o A : B : C : D =  \frac{1}{1}  :  \frac{1}{2} :  \frac{1}{4}  :  \frac{1}{8}  
 o = 8: 4 : 2 : 1 
• We need to arrange the sum in a way that it becomes 3 : 2
 o A and D with speed unit of 9
o B and C with speed unit of 6 .

Correct Answer: Option D

ScottTargetTestPrep · Answer

Solution:
 
Since A takes 4 days to complete the piece of work, then B, C, and D take 8 days, 16 days, and 32 days, respectively, to complete the same piece of work.

If one pair takes two-thirds the time needed by the second pair to complete the work, then their combined rate is three-halves the combined rates of the second pair (recall that rate is inverse of time). The rates of A, B, C, and D are 1/4, 1/8, 1/16, and 1/32, respectively.

Since 1/4 + 1/32 = 8/32 + 1/32 = 9/32 and 1/8 + 1/16 = 2/16 + 1/16 = 3/16 and 9/32 = 3/2 x 2/16, we see that the first pair must be A and D (and the other pair is B and C).

Answer: D

testtakerstrategy · Answer

This question, although relatively straightforward seems to take a lot of time. Is this an accurate problem?

Please discuss quicker ways to do this rather than just picking choices and plugging in.

Fdambro294 · Answer

I think the quickest methods are discussed. One key to make the problem move quickly is to realize that when the work being done is Constant, the Time needed to complete the work is Inversely Proportional to the Rates of work.

This is true for the Ratios as well.

Time Pair 1 to do job = 2/3 *(Time Pair 2 to do job)

Expressed in “ratio form”

Time Pair 1 to do job : Time Pair 2 to do job = 2 : 3

Since it is the same work being performed (Same 1 Job), the Ratio of Work Rates is Inversely Proportional

Rate of Work Pair 1 : Rate of Work Pair 2 = 3 : 2

Now you just need to Add 2 Rates for the Numerator and Add the other 2 Rates for the Denominator. There are only 6 different pairings of Rates that you need to add, and you just need to focus on the Rates in the Numerator that will have a higher Sum than the Rates in the Denominator.

This means the only Pairings that could work in the Numerator when you add the Rates are:

A + B 
Or
A + C 
Or 
A + D

When you test

(Rate of A + Rate of D) / (Rate of B + Rate of C) = (8/32 + 1/32)/ (4/32 + 2/32)

You will find the correct Ratio of 3/2

Using the Units Work Method outlined by CrackVerbal above would help you avoid fractions as well.

Posted from my mobile device

shirishgupta77 · Answer

I got the answer correct, but it took me close to 4min., to test values and come to an answer.
Is there some shortcut to it??

MathRevolution · Answer

A can complete a piece of work in 4 days: A = 1 work = 4 days

=> B = same work = 8 days

=> C = same work = 16 days

=> D = same work = 32 days

One pair =  \frac{2}{3}

=> A + D = 4 + 32 = 36 and B + C = 8 + 16 = 24

A + D = 36 *  \frac{2 }{ 3}  = 24

Answer D

Kinshook · Answer

A can complete a piece of work in 4 days: A = 1 work = 4 days

=> B = same work = 8 days

=> C = same work = 16 days

=> D = same work = 32 days

One pair = \(\frac{2}{3}\) [another pair]

=> A + D = 4 + 32 = 36 and B + C = 8 + 16 = 24

A + D = 36 * \(\frac{2 }{ 3}\) = 24 [B + C]

Answer D

Which is the first pair?

A can complete a piece of work in = 4 days
B can complete a piece of work in = 8 days
C can complete a piece of work in = 16 days
D can complete a piece of work in = 32 days

Part of work done by A in a day = 1/4
Part of work done by B in a day = 1/8
Part of work done by C in a day = 1/16
Part of work done by D in a day = 1/32

Total number of pairs = 4C2 = 6 = {(A,B), (A,C), (A,D), (B,C), (B,D), (C,D)}
Part of work done by (A, B) = 1/4 + 1/8 = 3/8
Part of work done by (A, C) = 1/4 + 1/16 = 5/16
Part of work done by (A, D) = 1/4 + 1/32 = 9/32
Part of work done by (B, C) = 1/8 + 1/16 = 3/16
Part of work done by (B, D) = 1/8 + 1/32 = 5/32
Part of work done by (C, D) = 1/16 + 1/32 = 3/32

Time taken by (A, B) to complete the work = 8/3 days
Time taken by (A, C) to complete the work = 16/5 days
Time taken by (A, D) to complete the work = 32/9 days
Time taken by (B, C) to complete the work = 16/3 days
Time taken by (B, D) to complete the work = 32/5 days
Time taken by (C, D) to complete the work = 32/3 days

32/9 = 2/3 * 16/3

First pair = (A, D); Second pair = (B, C)

IMO D

A can complete a piece of work in 4 days. B takes double the time take

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GMAT Problem Solving (PS) Questions

A can complete a piece of work in 4 days. B takes double the time take

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