Oliver Wyman – Numerical Reasoning Test
Had given the Oliver Wyman numerical reasoning test some time ago. The test is definitely not easy; I had expected analysis of some statistical graphs, data comprehension etc. But this test was completely unexpected. And you also get negatively marked for questions you get wrong, although you are allowed to skip questions.
Here are some of the sample questions that you can expect:
1. You have a jar filled with red, yellow and blue balls. What is the minimum number of balls you must pick out to guarantee 3 balls of the same color?
I think the answer is 7. Imagine worst case scenario – you pick 2 of each color. That makes 6 balls. The 7th ball you pick will ensure that you have 3 of the same color.
2. I have 19 bills totaling $215. The value of each bill is either $5 or $20. I have 9 bills in my pocket. What is range of money in my pocket?
Let’s say: Total number of $5 bills = x; this implies that Total number of $20 bills = 19-x
And we know that 5x + (19-x)*20 = 215 (This gives us 11 $5 bills & 8 $20 bills) Hence the total range is : $45 – $165 (9 $5 bills or 8 $20 bills + 1 $5 bill)
3. Whats the area of the shaded region if the length of a side of a square is l.
4. I shuffle a deck of cards and randomly pick one card and keep it aside. It is an Ace of Hearts. What is the probability that the next card I pick up is a heart or an ace?
5. An athlete has 75% of winning the race if he is not injured. If he is injured, his probability of winning the race is only 15%. If he total chances of winning is 51%, what is the probability that he gets injured?
6. A bakery sold 10 more cakes this month than it did the last month. It also sold 3 times as many cakes than the month before that. If that total number of cakes it sold in the last 3 months is 116, how many cakes did it sell this month?
7. What is the area of the shaded region given AB = 2 cm and CAB form a right angle?
I believe the answer is – Insufficient Data
8. I have a lawn that measures 9m by 5m. I dig a 1m flowerbed around it. What is the new area of my lawn?
9. I have a stock that is expected to grow 330% in the next 8 years. What is its average annual growth rate?
10. You have an equilateral triangle of length l that is divided into 9 smaller equilateral triangles. What is the total perimeter of the 9 triangles?
I a
m not sure about this one. I think the figure would look something like this, with each of the smaller triangles having a length of l/3. I wasn’t sure if we would recount the common sides as well. If we count every side of the triangles only once, I believe that we should get 6l as the total perimeter.
Any suggestions on how to do this one?
11. Currently, Country A’s energy demand is fulfilled by the following: Oil – 40%, Coal – 45% and Windmills – 450 total. The energy demand is expected to grow by 20% by next year. However, oil reserves are expected to go down by 10% and coal by 8%. How many more windmills will need to be built by next year to support the country growing energy demands?
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Tags: consulting interviews, Examples of Numerical Reasoning Questions, management consulting, Math Test, Numerical Reasoning, Numerical Reasoning Test, Oliver Wyman, Online Test, Quantitative Test
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May 5, 2011 at 10:10 am
i think the answer to 10 should be 9, as each triangle has a perimeter of 1.
May 5, 2011 at 10:12 am
oh and a question to you. why do u think the range in the second question is $45 – $165 (9 $5 bills or 8 $20 bills + 1 $5 bill)?
why not 45 – 180. there can be only 20ers in the pocket ..right? or were there any restrictions?
November 4, 2011 at 2:46 pm
If you had nine $20 bills in your pocket and the rest were $5 bills your total would be $230 which exceeds the total of $215.
Cheers
June 22, 2011 at 1:43 pm
#7, the answer should be area = pi( BC^2 – AC^2 ) = 4pi
November 16, 2011 at 4:27 pm
The diagram is flawed. According to it, BC=AB=2, this is in violation of the Pythagoras theorem. If you’re saying 4pi is the answer, its the answer to the area the outer circle only right?
November 16, 2011 at 4:28 pm
oops. my bad.. sorry for the confusion
July 21, 2011 at 10:44 am
10. There are 1 big triangle and 9 small. Big triangle side length = 1. On big triangle side placed 3 equal small triangles. So small triangle length = 1/3. Small triangle perimeter = 3*1/3 = 1. There are 9 small triangles with total perimeters = 9*1 = 9. Big triangle perimeter = 3*1 = 3. 3x times bigger perimeter.
October 28, 2011 at 1:08 pm
hey, I’ve got the OW test next week. Not too comfortable with these questions. What sort of material should I use to prepare. I have heard GMAT in other forums. What do you think?
November 7, 2011 at 3:42 pm
I just talked to somebody who did the online test, who confirmed, that these actual questions were part of it. Is the other parte made up by SHL style questions?
Anyway – thanks a lot for your insides.
BTW: Questions 7; 77 m2 ?
November 8, 2011 at 8:13 am
anyone got an answer key to these questions?
November 8, 2011 at 2:53 pm
Azoid!!!
What more did he/she told you about the test? some more questions?
why do you think that 7 is 77m`2??? is not 4*pi??did you mean question 8 maybe??
moreover…..what do you think is the result of number 5 and why??
thanks guys
November 18, 2011 at 7:20 am
Hi!
#5:
x=prob. injuried (1-x)=prob. not injuried
prob of winning=51%= 75%*(1-x)+15%*x —> x=40%
best
d
November 8, 2011 at 5:15 pm
Ive just done the OW tests and even after practicing the above for quite a while I still struggled ont he numeracy. Maybe answered about 10. Anyway these examples were a great help. An answer key would be v helpful though
January 28, 2012 at 8:32 am
What was the result for you Andey?
November 24, 2011 at 9:09 am
11. 828 windmills more (country A better be rich)
November 30, 2011 at 9:09 am
I think 828 is the right answer too
600 (new demand of 20%) + 228 (7.6% that oil and coal no longer supplies)
Anyone else get this answer
December 22, 2011 at 6:05 am
828 sounds right. Slightly different method:
Assuming 100 units of electricity currently, 40 units are supplied by oil, 45 units by gas and 15 units by 450 windmills.
So, first finding to use is 1 unit requires 30 windmills.
Then, for the following year, electricity demand has risen to 120 units. However, now, oil is only able to provide 36 units (10% decrease), and coal is able to provide 41.4 units (8% decrease). This implies that 42.6 units need to be provided by windmills.
42.6 x 30 = 1278 (i.e. 1278 – 450 = 828 extra windmills)
November 26, 2011 at 8:55 am
I’ve done them and my results are:
1- Insufficient Data
2- 45 – 165
3- 0.2146…
4- 29%
5- 40%
6- 54
7- ?
8- 60
9- 41.25%
10- 9
11 – 50.6%
November 28, 2011 at 3:48 pm
8 is wrong. It is 77 m2 ant not 60.
You are digging a 1m flowerbed around it so basically you get 1 m from left, 1 meter from right, 1 meter from up, 1 meter from down. Thats 2m extra to the height and 2m extra for the width, giving you h=11 and w=7
Answer is 77 m2.
Try to be sure about your answers before posting them please.
December 15, 2011 at 1:56 pm
This isn’t right Serge. The question says “I have a lawn that measures 9m by 5m. I dig a 1m flowerbed around it. What is the new area of my lawn?”
My lawn is exactly the same size. A flowerbed isn’t a lawn. Sounds like a trick question to me.
December 2, 2011 at 9:54 pm
9 is wrong too… very wrong. it says average annual growth rate not averaged growth over 8 years. ~41% a year is well over 1000% over 8 years.
December 22, 2011 at 6:00 am
You are right, the concept is similar to compound interest on savings accounts accrued annually. I think the calculation is something like this:
If the stock price increases by 330%, its actual value will be 430% (i.e. 4.3 times) of the initial value at the start of the 8 year period.
(x)^8 = 4.3
x = 1.20
This implies annual average growth rate is 20%.
Thus, if you start with a stock price of $1, it increases by 20% yoy, so after 8 years, the stock price will be $1 x (1.20)^8 = $4.30 (i.e. a $3.30 or 330% increase)
It is not a simple division problem (unfortunately).
December 22, 2011 at 7:51 pm
#9 is 16.1%
say x^8 = 3.3
therefore x = eigth root of 3.3.
= 1.161
Therefore 16.1% increase
December 22, 2011 at 5:51 am
Definitely insufficient data for Q7…
Q8 is tricky, probably not phrased well enough…
Answer to Q11 should be 828.
December 2, 2011 at 2:40 pm
Hello,
Tried to do the test only 8 questions answered for 20 minutes (don’t know which of them are right or wrong) – so it is definetly good way to pass the difficult ones during test taking.
The question is – can you skip a question and go back later to it if you have time left after the final one?
December 6, 2011 at 4:00 pm
I need some help in preparaing for consulting test. Please help me .. mssk.643@gmail.com
December 19, 2011 at 8:42 am
Q7: 4 pi is only valid if you assume that c is the centre of the inner circle. Is is valid to make such an assumption?
December 21, 2011 at 7:01 pm
Q11 – is 450 the total windmills or total energy demand?
Anyone got answer/explanation to Q9?
December 22, 2011 at 6:10 am
Q9) I think this is the calculation. If the stock price increases by 330%, its actual value will be 430% (i.e. 4.3 times) of the initial value at the start of the 8 year period.
(x)^8 = 4.3
x = 1.20
This implies annual average growth rate is 20%.
Thus, if you start with a stock price of $1, it increases by 20% y.o.y., so after 8 years, the stock price will be $1 x (1.20)^8 = $4.30 (i.e. a $3.30 or 330% increase)
As for Q11) I think the question is simply stating there are 450 windmills in total, supplying the remaining 15% of electricity demand. Just so people don’t get confused reading percentages of 40, then 45 and then suddenly 450…
Hope that helps!
January 5, 2012 at 4:18 pm
thanks engineer189!
Q11 makes a lot more sense this way!
re Q9
- I went the same route you did, but thought it impossible for them to expect one to calculate (x)^8=4.3 without a scientific calculator with such strict time limits
- also you seem to read it as if the stock was to “grow by 330% as opposed to “growing 330%” (using the same method you used it comes out as 16.1% as opposed to 20%)
- had an economist friend comment that our result is actually the compound annual growth rate as opposed to it being the average annual growth rate which is impossible to calculate without yearly averages
Anyone any further thoughts on this?
December 22, 2011 at 6:46 pm
Solution to question 7:
- CB is the radius of the bigger circle.
- If you extend CA to a point on the outer circle, D, then CB = CD. CDB is then an equilateral triangle.
- Equilateral means all angles = 60 degrees.
- Therefore angle ABC is 30 degrees.
- Using this information you can find length CA and hence solve the problem.
- CA = 2*tan(30) = 1.15cm
- CB = 2.31cm ( Using pythagoras)
- Shaded area = Big circle – small circle = pi*2.31^{2} – pi*1.15^{2}
Shaded Area = 12.61cms squared
Convinced its right. Tell me what you think?
January 4, 2012 at 8:48 pm
Why is CBD an equilateral triangle? It is only an isosceles triangle, because CB=CD, and we don’t know if DB is equal to CB/CD. I also think that the anwer is insuffisient data. We even don’t know if CA is a radius.
January 5, 2012 at 4:21 pm
BooYeah! as in the previous solution you assume that C is in the centre of the cirles – as Swa pointed out – there’s nothing in the drawing/text to confirm such assumption..
January 9, 2012 at 2:43 am
You’re right. I tried solving it assuming that the C is the centre.
How did your online tests go?…If I got this question I think would have just skipped it because of negative marking.
January 8, 2012 at 8:50 pm
how can you be sure the CDB is an equilateral triangle though?
January 5, 2012 at 7:53 pm
CDB is then an equilateral triangle. == Wrong , DB is a chord and is not equal to CD=CB , ie. DB!=CD and DB!=CB
January 9, 2012 at 2:30 am
Check out the diagram this page:
http://www.sonoma.edu/users/w/wilsonst/courses/math_150/gw/citt.html
As the second point on this diagram shows, if AB (on our diagram) bisects CD at right angles, then triangle CDB must at least be an isosceles triangle where point B will be the vertex.
Therefore, lengths CB and DB must be the same.
Since we already know that CD and CB are the same length, then all the sides are the same length, which means that it is an equilateral triangle.
Does that make it
January 9, 2012 at 2:33 am
Don’t know how to edit posts lol. Didnt mean to write ‘Does that make it’.
January 9, 2012 at 2:44 am
Btw have any of you guys been invited for interviews?….They said that my application is on hold until the 12th..
January 25, 2012 at 8:54 pm
are thery the same questions from the real OW test?