Quant Boosters  Soumya Chakraborty  Set 3

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
After the 15% discount over 30, the new SP would have been 25.5.
But the shopkeeper returns a sachet worth rs. 1.5 to the customer, so the net SP = 24
CP = 24/1.2 = 20

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q9) A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Profit of 100 = SP of 75
Thus, P/SP = 75/100
If P = 75, SP = 100, CP = 25
Thus, P/CP = 75/25, or 300%

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q10) The fees of a school increased 9.09%, then by 8.33%, and then by 7.69% over 3 years. If the current school fees is Rs. 3,360, then find the approximate school fees 3 years back.

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
The multiplication factors are:
9.09% increase = 12/11
8.33% increase = 13/12
7.69% increase = 14/13
So, the value becomes
(12/11) * (13/12) * (14/13) = 14/11
14 is the new part so that corresponds to 3360 = 14 * 240
11 should then correspond to 2640 (=11 * 240)

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q11) A student scored 43% in an exam and failed by 12 marks. Another student scored 48% marks in the same exam and passed by 18 marks. Find the passing percentage in the exam.

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
The percentage points difference is 5%, which corresponds to 30 marks
So each percentage point should be 6 marks. Now, someone who failed by 12 marks, must have failed 2 percentage points. As, he gets 43%, the passing percentage must be 45%

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q12) In September 2009, the sales of a product were 2/3rd of that in July 2009. In November 2009, the sales of the product were higher by 5% as compared to September 2009. How much is the percentage of increase in sales in November 2009 with respect to the base figure in July 2009.

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
5% increase = 21/20
So, effectively = (2/3) * (21/20) = 7/10, which implies a reduction of 3/10 = 30% decrease

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q13) The length, breadth and height of a room are in ration 3:2:1. The breadth and height of the room are halved and length of the room is doubled. Then area of the four walls of the room will
a) Decrease by 13.64%
b) Decrease by 15%
c) Decrease by 18.75%
d) Decrease by 30%

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
I don't like unnecessary fractions. As we are about to half the breadth and height, so let us keep these two values EVEN number to begin with
Length = 6
Breadth = 4
Height = 2
Area of the four walls, initially = (6+4) * 2 * 2 = 40
New values
L = 12
B = 2
H = 1
Area of four walls, new = (12+2) * 1 * 2 = 28
Reduction = 12/40 = 30%

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q14) The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Increased by 25%, multiplication factor of 5/4
Reduced by 30%, multiplication factor of 7/10
As, we are dealing with the same number, let us find the difference between these two fractions
5/4  7/10 = 25/20  14/20 = 11/20
11 corresponds to 22
Thus, 20 corresponds to 40
I have purposely added few extra steps to enable you to understand how i calculate these mentally

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q15) Wheat is now being sold at Rs 27 per kg. During last month its cost was rs 24 per kg. Find by how much percent a family reduces its consumption so as to keep the expenditure fixed.

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Just reverse the multiplying factor here.
AS the price becomes 27/24 = 9/8
The consumption must become 8/9 to keep the expenditure constant
So, the reduction must be 1/9 = 11.11%
You can also treat this as a proportionality question, where price and consumption are inversely proportional.

Soumya Chakraborty last edited by Soumya Chakraborty
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q16) For how many values of 'n' in the range of 1 to 1000, does 2^(2^n) when divided by (2^n  1) leave a remainder of 1 ?

Soumya Chakraborty last edited by Soumya Chakraborty
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
If 2^(2^n) when divided by 2^n  1 leaves a remainder of 1
It implies that 2^(2^n)  1 must be divisible by 2^n  1
a^x  b^x is divisible by a^y  b^y, only if x is divisible by y
Thus in the question 2^n must be divisible by n
Only possible if n is also a power of 2
You can't consider n = 2^0 = 1
In that case 2^n  1 = 1
If the divisor is 1, that can't leave a remainder
So in the range we have, 2^1 to 2^9 ... Nine possibilities

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q17) A bakery opened with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 60% of the remaining rolls were sold between noon and closing time. How many dozen rolls were left unsold?

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
50% + 60% of 50% are gone = 80% gone
left with 20% of 40 = 8

Soumya Chakraborty last edited by
CAT 2017  QA 100 Percentile  IIM Lucknow  Managing Partner  MathOratory
Q18) If (3x+2y)/(3x2y) = 5/2, Find (5x+4y)/(7x2y)