Google Placement Papers

Google Technical Aptitude paper 2015



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Google Reasoning Questions 2014

Posted on :02-02-2016
Q1. Principles and Practices of Management :

How will you influence people to strive willingly for group objectives in your organization (target based industry)? Apply interpersonal influence through communication process towards attaining your personalized goals?

Q2. Human Resources Management :

The present state of recession in the IT Industry  as a Human Resource Manager how are you going to undertake Human Resource Planning to Macro level to tide over the crisis

Q3. Financial Management :

What will your outlook towards maintenance of liquid assets to ensure that the firm has adequate cash in hands to meet its obligation at all times?

Q4. Marketing Management :

If you are working in a super market, what techniques/ tools you will use in data collection. How are you going to analysis the data and make inferences? How will you finally apply your market research to improve sales and win over customers?

Q5. Organizational Behaviour:

 If you are made the compaign leader for a particular political party .How will you use your leader ship skills to motivate your party men to ensure success of the party nominee in the elections? (Focus on the individual motivate and apply leadership style).

Q6. Principles of Economics :

Suppose the price elasticity of demand for the textbooks is two and the price of the textbook is increased by 10% By how much does the quantity demand fall? 

Q7. Enter the results and discuss reason for the fall in quantity demand. There are 8 balls that look identical. One of them weighs less than the others. Given a weighing scale, how will you find this ball. There are 3 baskets of fruits with wrong lables, one basket has apple, another basket has orange,another has combination of apple and orange,what is the least way of interchange the lables.

Q8. Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number. There are N egg baskets and the number of eggs in each basket is a known quantity.

Q9. Two players take turns to remove these eggs from the baskets. On each turn, a player must remove at least one egg, and may remove any number of eggs provided they all belong to the same basket. The player picking the last egg(s) wins the game. If you are allowed to decide who is going to start first, what mathematical function would you use to decide so that you end up on the winning side?


Q10. This can be solved through systematic application of logic. For example, cannot be equal to 0, since . That would make , but , which is not possible. Here is a slow brute-force method of solution that takes a few minutes on a relatively fast machine:

This gives the two solutions :
777589 - 188106 == 589483
777589 - 188103 == 589486

Q11. Here is another solution using Mathematics Reduce command:

Q12. A faster (but slightly more obscure) piece of code is the following:
Faster still using the same approach (and requiring ~300 MB of memory):
Even faster using the same approach (that does not exclude leading zeros in the solution, but that can easily be weeded out at the end):
Here is an independent solution method that uses branch-and-prune techniques: And the winner for overall fastest:

Q13. Write a haiku describing possible methods for predicting search traffic seasonality. MathWorlds search engine seemed slowed this May. Undergrads prepping for finals.

Q14.

1
1 1
2 1
1 2 1 1
1 1 1 2 2 1

Whats the next line?

ANS: 312211.

Q15. This is the "look and say" sequence in which each term after the first describes the previous term: 

one 1 (11); 
two 1s (21); 
one 2 and one 1 (1211); 
one 1, one 2, and
two 1s (111221); and so on. 

See the look and say sequence entry on MathWorld for
a complete write-up and the algebraic form of a fascinating related quantity known as Conveys constant.

Q16. You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling around. What does though do?

A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.
B) Use the laptop as a digging device to tunnel to the next level.
C) Play MPoRPG until the battery dies along with your hopes.
D) Use the computer to map the nodes of the maze and discover an exit path.
E) Email your resume to Google, tell the lead gnome you quit and find yourself in whole different world [sic].


Q17. Whats broken with Unix?

ANS: Their reproductive capabilities.


Q18. On your first day at Google, you discover that your cubicle mate wrote the textbook you used as a primary resource in your first year of graduate school. Do you:

A) Fawn obsequiously and ask if you can have an autograph.
B) Sit perfectly still and use only soft keystrokes to avoid disturbing her
concentration
C) Leave her daily offerings of granola and English toffee from the food bins.
D) Quote your favorite formula from the textbook and explain how it
s now your mantra.
E) Show her how example 17b could have been solved with 34 fewer lines of code.

Q19. Which of the following expresses Googles over-arching philosophy?

A) "Im feeling lucky"
B) "Dont be evil"
C) "Oh, I already fixed that"
D) "You should never be more than 50 feet from food"
E) All of the above

Q20. How many different ways can you color an icosahedron with one of three colors on each face?

For an asymmetric 20-sided solid, there are possible 3-colorings . For a symmetric 20-sided object, the Polya enumeration theorem can be used to obtain the number of distinct colorings. Here is a concise Mathematics implementation: What colors would you choose?

Q21. This space left intentionally blank. Please fill it with something that improves upon emptiness. For nearly 10,000 images of mathematical functions, see The Wolfram Functions Site visualization gallery.

Q22. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knights move away? 

This problem is discussed in J. Csertis 1999 arXiv preprint . It is also discussed in The Mathematics GuideBook for Symbolics, the forthcoming fourth volume in Michael Trotts GuideBook series, the first two of which were published just last week by Springer-Verlag. The contents for all four GuideBooks, including the two not yet published, are available on the DVD distributed with the first two GuideBooks. 11. Its 2PM on a sunny Sunday afternoon in the Bay Area. Youre minutes from the Pacific Ocean, redwood forest hiking trails and world class cultural attractions. What do you do?

Q23. In your opinion, what is the most beautiful math equation ever derived?  There are obviously many candidates. The following list gives ten of the authors favorites:

1. Archimedes recurrence formula : , , ,
2. Euler formula :
3. Euler-Mascheroni constant :
4. Riemann hypothesis: and implies
5. Gaussian integral :
6. Ramanujans prime product formula:
7. Zeta-regularized product :
8. Mandelbrot set recursion:
9. BBP formula :
10. Cauchy integral formula:

Q24. An excellent paper discussing the most beautiful equations in physics is Daniel Z. Freedmans " Some beautiful equations of mathematical physics ." Note that the physics view on beauty in equations is less uniform than the mathematical one. To quote the not necessarily- standard view of theoretical physicist P.A.M. Dirac, "It is more important to have beauty in ones equations than to have them fit experiment."

Q25. Which of the following is NOT an actual interest group formed by Google employees?

A. Womens basketball
B. Buffy fans
C. Cricketers
D. Nobel winners
E. Wine club

Q25. What will be the next great improvement in search technology?

Semantic searching of mathematical formulas.
underway at Wolfram Research that will be made available in the near future.

Q26. What is the optimal size of a project team, above which additional members do not contribute productivity equivalent to the percentage increase in the staff size?

A) 1
B) 3
C) 5
D) 11
E) 24

Q27. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.) This is the isoperimetric point , which is at the center of the larger Soddy circle. It is related to Apollonius  problem . The three tangent circles are easy to construct: The circle around has diameter , which gives the other two circles. A summary of compass and straightedge constructions for the outer Soddy circle can be found in " Apollonius  

Problem: A

Study of Solutions and Their Connections" by David Gisch and Jason M. Ribando.

Q28. Consider a function which, for a given whole number n, returns the number of ones required when writing out all numbers between 0 and n. 

For example, f(13)=6.
Notice that

f(1)=1. What is the next largest n such that
f(n)=n?

Q29. What number comes next in the sequence: 10, 9, 60, 90, 70, 66, ?



  
   






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