MBA Crystal Ball

Hi avrgmat,

Here are some sample GMAT questions on topics you mentioned in your previous post:

DS (Statistics)

What was the standard deviation of the scores obtained by the residents of Brashville in 2003 on the Scamford-Skinnett Intelligence Quotient test if the standard deviation of the scores of the same residents in 2002 in the same test was 2?

1) The mean score obtained by the residents of Brashville in 2003 on the Scamford-Skinnett Intelligence Quotient test was 22
2) The scores of each resident of Brashville on the Scamford-Skinnett Intelligence Quotient test in 2003 were 10% more than their scores in 2002 in the same test

PS motion

It takes Ann 4 hours and 15 minutes to go 35 miles downstream in her motorboat and go back the same distance upstream. If the rate of the motorboat in still water is 17 miles per hour, what is the speed of the current?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

PS work problem

Bob and his wife Julie take 1 week to empty a 40-liter barrel of clear water. Julie and her daughter Jane can empty the same barrel in 2 weeks. Bob and Jane take 1.2 weeks to empty it. How many barrels of water do they need for a 30-day month?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Everybody is welcome to try solving the questions!

P.S. Regarding 2 previous questions, avrgmat, you were totally right! Keep practising!

Thanks GoGMAT team.

I have taken a shot at these 3 questions and personally, these were way tough for me. Maybe I am not up to the mark on these topics or then these problems were simply way out of my league. I am not sure if I have answered any correctly. :( Here's my response.

1. DS - Statistics

For standard deviation, we need the mean and the numbers in the given set. We have been give the standard deviation of 2002 as 2.

(i) We have information about the mean score of 2003 but no information on the individual scores.

So statement (i) is insufficient.

(ii) Here we have information that the scores in 2003 have all increased by 10% from 2002. Since all scores have improved by 10% it would mean that the mean and the standard deviation have changed. But we still do not have any info on the scores of 2003.

So statement (ii) is insufficient.

(i) and (ii) together also does not give any info on the score of 2003. So both together are insufficient. The answer therefore is E.

I have an observation here. If instead of the 10% increase on scores, we would have had a fixed value of growth, eg. each students marks grew by say 2 marks then the standard deviation would in 2003 would be same as 2002. Please let me know if this observation is correct.

It took me 2:24 mins and I would say that I would be happy if I am correct on this question.

2. PS - Motion

This one was even tougher. I was caught between calculating and approximating. In the end I ended up guessing after spending ~3.20 mins. :(

Speed in still water = 17 mph
Total Distance = 35 miles

I followed the approach of plugging in the answer choices.

started with choice A because it seemed like making the calculation of a bit easy since 35 is a factor of 7 and 5.

A = speed of current : 3

Downstream : Speed = 17+3 = 20 mph, time taken for 35 miles = (35/20) = 7/4 = 1 + 3/4 i.e. 1 hr 45 mins.

Upstream : Speed = 17-3 = 14 mph, time taken for 35 miles = (35/14) = 5/2 = 2 hr 30 mins.

Incidentally this sums up to 4 hr 15 mins.

Answer = A

I had reached almost 3 mins at this stage and decided to go ahead with the guess of A rather than confirm this by plugging in another choice. I am sure that this was beyond my capability to solve in 2 mins if this question would have crops up in the actual GMAT.

3. PS - Work Problem

This problem totally hit through the roof for me. :( Once again took significantly higher time than 4 mins.

I was getting confused between approximating and plugging in some numbers for the variables. I again ended up guessing for this question.

Bob + Julie = 1 week = 40 liters

Bob + Jane = 2 weeks = 20 liters

Bob + Jane = 1.2 week = 40 liters

This took a while but the only values I could quickly think of for the first two equations were -:

Bob = 25 litres, Julie = 15 litres and Jane = 5 litres

Thus in 1 week they need 45 litres in total i.e. ~6.5 per day.

so for 30 days it is 30*6.5 = ~195 i.e. 5 barrels.

The answer is B.

Please advise on the most efficient and quickest way to solve all these 3 problems within 2 mins.

Hi avrgmat,

below are my notes with straightforward reasoning how I would solve these problems.

1. DS - Statistics

(1) Knowledge of the mean score does not allow us to calculate the standard deviation without knowledge of of the individual scores. Thus, the statement alone is unsufficient.

(2) This statement states that if {x1, x2, ..., xn} is the set of residents' scores of Brashville in 2002 then {1.1*x1, 1.1*x2, ..., 1.1*xn} is the set of residents' scores of Brashville in 2003. Therefore, according to the linear property of standard deviation, the standard deviation in 2003 will equal 1.1*2 = 2.2. B is the answer.

2. PS - Motion

Let Vm miles per hour be the speed of the motorboat and Vc miles per hour be the speed of the current.
Then we have the folloving equation:

35*(1/(Vm+Vc) + 1/(Vm-Vc)) = 17/4

Multiplying each side by 4*(Vm-Vc)*(Vm+Vc), we get

140*(Vm - Vc + Vm + Vc) = 17*(Vm-Vc)*(Vm+Vc)
280*Vm = 17*Vm^2 - 17*Vc^2
17*Vc^2 = 17*Vm^2 - 280*Vm

as we know Vm = 17 so we have

Vc^2 = 17^2 - 280 = 289 - 280 = 9
Vc = 3. A is the answer.

3. PS - Work problem

Let Vb liters per day is the work speed of Bob; Vjul liters per day is the work speed of Julie and Vjan liters per day is the work speed of Jane. Then we have the following system of linear equations:

Vb + Vjul = 40/7
Vjul + Vjan = 40/14 = 20/7
Vb + Vjul = 400/84 = 100/21

Subtracting the second equation from the first equation, we get

Vb - Vjan = 20/7

Summing up this equation and third equation above we get

2*Vb = 160/21 and thus Vb = 80/21 then Vjul = 40/21 and Vjan = 20/21.
Therefore, for a 30-day month period they will need:
30*(80/21 + 40/21 + 20/21) = 30*140/21 = 10*20 = 200 liters of water or 5 40-liter barrels. B is the answer.

Hope these notes are helpful.

galina_gmat,

Thank you for your detailed explanation and thoughts!

To everyone,
Here is another portion of GMAT questions for you to train your brains and practice!

Problem Solving

Ann worked for a certain company for a year. If Ann’s average monthly salary was $1,200 and her median monthly salary was $1,000, which of the following statements must be true?
I. At least one of the monthly salaries was greater than $1,350
II. At least one of the monthly salaries was greater than $1,000 and less than $1,200
III. At least one of the monthly salaries was less than $1,000

(A) None
(B) I only
(C) II only
(D) III only
(E) I and II

Data Sufficiency

If an employee from Red State Reserve Bank is chosen at random, what is the probability that the employee is either male or over 31 years old?

1. The probability that the employee is male minus the probability that the employee is over 31 years old is 0.14
2. The probability that the employee chosen at random is male plus the probability that the employee chosen at random is over 31 years old is 0.48

Taking a shot at the above two quant problems.

1. PS. Found myself re-looking at the answers, tried to solve and ended up guessing.

Given info is :

Average = 1200 per month
Total = 1200*12 = 14400

For Median, the salaries need to be placed in ascending order.

Median = 1000 i.e. (6th month + 7th month)/2 = 1000
Hence salary of 6th month + 7th month = 2000

We have to find "Must Be True" i.e. Have To Be True

Started with III since I found it easy.

(III) It is possible that all of the salaries till till the 7th Month were 1000. The remaining months can make up for the (14400-7000). So this does not have to Be True. This may or may not be true.

(II) Once again, if the first seven months have 1000 each then the remaining last 5 months have to equal 7400. They could have equal value of (7400/5) i.e. 1280.

Thus this may or may not be true i.e. Does Not Have to be true.

Effectively we have to now choose between A and B.

(I) This was a real tricky one.

Using the logic for (II) this need not be true.

So i ended up guessing on answer as (A) i.e. None.

2. DS

Another tough question personally. Guessing game again. :)

P(M) = probability that the chosen employee is male.

P(T) = probability that the chosen employee is 31+ years.

To find : P(M or T) = P(M) + P(T) - P(M and T)

(i) P(M) - P(T) = 0.14. No information about P(M and T). So insufficient.

Hence Answer is B,C or E.

(ii) P(M) + P(T) = 0.48. No information on P(M and T). So insufficient.

Solving together, we get values of P(M) and then P(T) but not on P(M and T). Was around 2.5 mins at this time. So guessed on E.

Answer for this question chosen by me was E.

Looking forward to your responses.

Hi GoGMAT Team,

I really find the questions testing the application of my concepts but I am not sure if I will be able to solve the questions in around 2 mins.

It would really helpful if you could mention the difficulty level of the problems when you provide solutions for these questions.

Hi avrgmat,

your reasoning is clear and almost correct.

With respect to the first PS problem, there was one calculating mistake: namely, 7400/5 = 1480 not 1280 as was mentioned. Having this in mind, surely you would get the right answer to this problem quickly.

And below are some notes:

We would also started here with counterexamples.

(|||) and (||) we could even check that all of the salaries till 11 Month were 1000 and the last salary was 14400-11000=3400. Thus, (|||) and (||) statements do not have to be true.

(|) The example above works for this statement. For general conclusion here we could use the logic simiral to yours for (||) statement. Then we consider that all the salaries till the 7 Month were 1000 and then the remaining last 5 Months have to equal 7400. They could have equal value of 7400/5=1480, and it would be average salary for the last remaining 5 Months. In other words, even if four salaries were less than 1350, the last salary value must have been much greater than 1480 to balance the average value. Thus, at least one of the monthly salaries was greater than 1350. This statement must be true.
Alternative approach here is to consider that all salaries till the 7 Month were 1000 and all the salaries for the remaining last 5 Months were 1350. Then we could have

1000*7 + 1350*5 = 7000 + 6750 = 13750

but this value would be less then our total value of 14400. Thus at least one of the salaries value was greater than 1350 in our example. This statement must be true.
The answer is B.

With respect to the second DS problem your reasoning and the answer are correct, we would solve this queston in quite similar way just with different variables.

These GMAT questions are from medium to hard difficulty. It is assumed that it is possible to solve them in 2-3 mins if you know the method.

Hi everone!

Here is our next question for you to train your brains:

Problem Solving


A manager hired 4 employees to complete a certain project in 15 days. After 10 days of work the employees completed only half of the project. How many additional employees should the manager hire to finish this project in time if each employee works at the same constant rate?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Personally, this has been without doubt one of the less difficult problems given out by GoGMAT. :D

Without going into calculations, I tried using the more logical approach.

Expected --: 15 days - 4 workers will need to complete the job.

After 10 days --: they should have completed 2/3 of the job but instead were able to completed only 1/2 of the job.

Hence they completed 25% of total job per 5 days.

Balance work remaining = 1/2.
Balance days = 5

These 4 workers will complete 1/4 of the job in 5 days.

Hence we need 4 more workers to complete the 1/4 of the remaining job in 5 days.

I will choose D.

Hi avrgmat,

You are right!

We will try to post harder questions :)