Quantitative Ability-3

41. The relationship between base 10 and base ‘e’ in log is given by log10N = 0.434 logeN

42. WINE and WATER formula

Let Q - volume of a vessel, q - qty of a mixture of water and wine be removed each time from a mixture, n - number of times this operation is done and A - final qty of wine in the mixture, then,

A/Q = (1-q / Q)^n

43. Pascal’s Triangle for computing Compound Interest (CI)

The traditional formula for computing CI is
CI = P*(1+R/100)^N – P

Using Pascal’s Triangle,

Number of Years (N)
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
… 1 .... .... ... ... ..1

Eg: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1:
Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331

The coefficients - 1,3,3,1 are lifted from the Pascal's triangle above.

Step 2:
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331 (leaving out first term in step 1)

If N =2, we would have had,
Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs.1210
CI = 2 * 100 + 1* 10 = Rs.210

44. Suppose the price of a product is first increased by X% and then decreased by Y% , then, the final change % in the price is given by:
Final Difference% = X - Y - XY/100

Eg) The price of a T.V set is increased by 40 % of the cost price and then is decreased by 25% of the new price. On selling, the profit made by the dealer was Rs.1000. At what price was the T.V sold?

Applying the formula,
Final difference% = 40 – 25 - (40*25/100) = 5 %.

So if 5 % = 1,000
Then, 100 % = 20,000.
Hence, C.P = 20,000
& S.P = 20,000+ 1000= 21,000

45. Where the cost price of 2 articles is same and the mark up % is same, then, marked price and NOT cost price should be assumed as 100.

-> Where ‘P’ represents principal and ‘R’ represents the rate of interest, then, the difference between 2 years’ simple interest and compound interest is given by P * (R/100)2

-> The difference between 3 years’ simple interest and compound interest is given by (P * R2 *(300+R))/1003

-> If A can finish a work in X time and B can finish the same work in Y time then both of them together can finish that work in (X*Y)/ (X+Y) time.

-> If A can finish a work in X time and A & B together can finish the same work in S time then B can finish that work in (XS)/(X-S) time.

-> If A can finish a work in X time and B in Y time and C in Z time then all of them working together will finish the work in (XYZ)/ (XY +YZ +XZ) time

-> If A can finish a work in X time and B in Y time and A, B & C together in S time then
· C can finish that work alone in (XYS)/ (XY-SX-SY)
· B+C can finish in (SX)/(X-S); and
· A+C can finish in (SY)/(Y-S)

48. In case ‘n’ faced die is thrown k times, then, probability of getting atleast one more than the previous throw = nC5/n5

-> When an unbiased coin is tossed odd no. (n) of times, then, the no. of heads can never be equal to the no. of tails i.e. P (no. of heads=no. of tails) = 0

-> When an unbiased coin is tossed even no. (2n) of times, then, P (no. of heads=no. of tails) = 1-(2nCn/22n)

50. Where there are ‘n’ items and ‘m’ out of such items should follow a pattern, then, the probability is given by 1/m!

Eg) 1. Suppose there are 10 girls dancing one after the other. What is the probability of A dancing before B dancing before C?

Here n=10, m=3 (i.e. A, B, C)

Hence, P (A>B>C) = 1/3!
= 1/6

Eg)2. Consider the word ‘METHODS’. What is the probability that the letter ‘M’ comes before ‘S’ when all the letters of the given word are used for forming words, with or without meaning?

P (M>S) = 1/2!
= 1/2


-> Calendar repeats after every 400 years.

-> Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.

-> Century has 5 odd days and leap century has 6 odd days.

-> In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.

-> January 1, 1901 was a Tuesday.

-> For any regular polygon, the sum of the exterior angles is equal to 360 degrees, hence measure of any external angle is equal to 360/n (where n is the number of sides)

-> For any regular polygon, the sum of interior angles =(n-2)*180 degrees
So measure of one angle is (n-2)/n *180

-> If any parallelogram can be inscribed in a circle, it must be a rectangle.

-> If a trapezium can be inscribed in a circle it must be an isosceles trapezium (i.e. oblique sides equal).

53. For an isosceles trapezium, sum of a pair of opposite sides is equal in length to the sum of the other pair of opposite sides (i.e. AB+CD = AD+BC, taken in order)

-> For any quadrilateral whose diagonals intersect at right angles, the area of the quadrilateral is
0.5*d1*d2, where d1, d2 are the length of the diagonals.

-> For a cyclic quadrilateral, area = root((s-a) * (s-b) * (s-c) * (s-d)), where s=(a + b + c + d)/2
Further, for a cyclic quadrilateral, the measure of an external angle is equal to the measure of the interior opposite angle.

-> Area of a Rhombus = Product of Diagonals/2

55. Given the coordinates (a, b); (c, d); (e, f); (g, h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for
[(a + e)/2, (b + f)/2] = [(c + g)/2, (d + h)/2]

56. Area of a triangle

-> 1/2*base*altitude
-> 1/2*a*b*sin C (or) 1/2*b*c*sin A (or) 1/2*c*a*sin B
-> root(s*(s-a)*(s-b)*(s-c)) where s=(a+b+c)/2
-> a*b*c/(4*R) where R is the circumradius of the triangle
-> r*s ,where r is the inradius of the triangle

57. In any triangle
-> a=b*cos C + c*cos B
-> b=c*cos A + a*cos C
-> c=a*cos B + b*cos A
-> a/sin A=b/sin B=c/sin C=2R, where R is the circumradius
-> cos C = (a^2 + b^2 - c^2)/2ab
-> sin 2A = 2 sin A * cos A
-> cos 2A = cos^2 (A) - sin^2 (A)

58. The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1

59. Appollonius Theorem

In a triangle ABC, if AD is the median to side BC, then
AB2 + AC2 = 2(AD2 + BD2) or 2(AD2 + DC2)

-> In an isosceles triangle, the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.

-> In any triangle the angular bisector of an angle bisects the base in the ratio of the other two sides.

61. The quadrilateral formed by joining the angular bisectors of another quadrilateral is always a rectangle.

62. Let W be any point inside a rectangle ABCD, then,
WD2 + WB2 = WC2 + WA2

63. Let a be the side of an equilateral triangle, then, if three circles are drawn inside this triangle such that they touch each other, then each circle’s radius is given by a/(2*(root(3)+1))

-> Distance between a point (x1, y1) and a line represented by the equation ax + by + c=0 is given by ax1+by1+c/Sq(a2+b2)
-> Distance between 2 points (x1, y1) and (x2, y2) is given by Sq((x1-x2)2+ (y1-y2)2)

65. Where a rectangle is inscribed in an isosceles right angled triangle, then, the length of the rectangle is twice its breadth and the ratio of area of rectangle to area of triangle is 1:2.

General Awareness Test 2017

Total Time allotted for Test = 40 Minutes, Timer : 00:00

General Awareness Test 2017 for MBA Exams like XAT

General Awareness 2017 - Questions 1 - 60

3 Marks for each right answer and -1 Mark for each wrong answer.
Total Marks = 180

Q1. 'The Great Indian Novel' is a book written by:

Q2. In which year was the 'All India Radio' set up?

Q3. Who wrote the line: ' A thing of beauty is a joy forever'?

Q4. Entomology is the science that studies ?

Q5. Who is the current CEO & MD of Infosys?

Q6. Periyar Tiger Reserve is located in which state?

Q7. Capital of Australia is:

Q8. How many Gold Medals did India win in 2014 Commonwealth game?

Q9. Which country hosted 2016 Olympics?

Q10. Who among the following has become the first Indian to be honoured with Harvard Medal?

Q11. The total cost of the India's Mars Orbitor Mission is:

Q12. Who is the going to be the new chief justice of India from 4th January 2017?

Q13. How much was India's Growth Rate in 2015-16?

Q14. If the cash reserve ratio is lowered by the RBI, its impact on credit creation will be to

Q15. Excise duty is a tax levied on the

Q16. Who among the following has been appointed the National Security Advisor (NSA) to the Prime Minister of India?

Q17. Which of the following technology firms unveiled a prototype driverless car, recently?

Q18. Finance Commission is constituted every:

Q19. Census of India is conducted every ____ Years and lastly it was done in ____

Q20. Which film won the best picture Oscar award in 2016:

Q21. Who is current President of world bank:

Q22. Who is the present CEO of Apple?

Q23. The state which has the highest sugarcane production in India is

Q24. The mineral in which India depends largely on imports is

Q25. Indian general election of 2014 was held to constitute the 16th Lok Sabha, electing members of parliament for parliament. How many total constituencies / seats are there in current Lok Sabha?

Q26. Telangana is ___ state of India and its Capital is ____

Q27. Who is current Director-General of WTO

Q28. Which company acquired online fashion portal Myntra.Com in 2014

Q29. Who won 2016 nobel prize for Peace?

Q30. Who among the following has been named as the TIME magazine Person of the Year 2016?

Q31. Which Indian village has recently earned the tag of becoming India’s first digital village in India?

Q32. Who was recently elected as the President of FICCI for the year 2017?

Q33. Name the Indian states that have jointly topped the Ease of Doing Business Reforms Ranking 2015-16??

Q34. Who was recently selected by the UN Security Council as the next UN Secretary-General?

Q35. Which country has topped the Global Competitiveness Index, GCI 2016-17 released in September 2016.?

Q36. Who is appointed as the Chairman of Life Insurance Corporation (LIC) of India?

Q37. Which stock exchange became the first Indian stock exchange to file Initial Public Offering with SEBI?

Q38. Which of the following Indian Actress has been ranked 10th in the world in the list of “Forbes magazine”?

Q39. Who is recently appointed as the Managing Director of the State Bank of India?

Q40. Which company has acquired Yahoo for $4.8 billion in July 2016?

Q41. Who has been elected as the Chairman of the International Chamber of Commerce (ICC)?

Q42. Who has been elected and appointed as the new President of Taiwan?

Q43. Who has been declared as the new Chief Minister of Assam?

Q44. Which is the 1st country of the world to put a ban on Deforestation?

Q45. Who among the following headed the 7th Pay Commission?

Q46. Who of the following was not selected for 2016 Rajiv Gandhi Khel Ratna?

Q47. Who was sworn in as President of Brazil in August 2016?

Q48. Majuli recently became the first island district of India. Majuli is located in which of the following states?

Q49. Who among the following has topped the Forbes 2016 list for “World's Most Powerful People”?

Q50. When is Constitution Day celebrated in India to spread awareness about Indian Constitution?

Q51. Who is the author of the book titled “An Era of Darkness: The British Empire in India” that was recently released by released by the Vice President of India M. Hamid Ansari

Q52. Who among the following is appointed as CEO of the World Bank?

Q53. Who among the following won the 2016 Nobel Prize in Literature?

Q54. Who of the following will be the Chief Guest at the Republic Day celebrations on 26 January 2017?

Q55. Who was recently sworn in as the Governor of Punjab?

Q56. Which Indian state has recently abolished Agricultural Income Tax?

Q57. Which state celebrated the bicentenary (200 years) of the 1817 Paika revolt against the British Empire in 2016?

Q58. Which Indian para-athlete recently became the first Indian to win two gold medals at the Paralympics?

Q59. Name the film that has been selected as India's entry to the 89th Academy Awards (Oscars) to be held in 2017 in the Foreign Language Film category.

Q60. Which movie won the Best Film Award at the first BRICS Film Festival that recently concluded in New Delhi?