# Quant Boosters - Soumya Chakraborty - Set 3

• 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)

• 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.

• 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%

• 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.

• 5% increase = 21/20
So, effectively = (2/3) * (21/20) = 7/10, which implies a reduction of 3/10 = 30% decrease

• 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%

• 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%

• 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?

• 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

• 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.

• 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.

• 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 ?

• 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

• 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?

• 50% + 60% of 50% are gone = 80% gone
left with 20% of 40 = 8

• Q18) If (3x+2y)/(3x-2y) = 5/2, Find (5x+4y)/(7x-2y)

• Apply Componendo Dividendo, to get
3x/2y = 7/3
or, x/y = 14/9
In order to find (5x+4y)/(7x-2y), simply substitute 'x' with 14 and 'y' with 9
So the reqd answer is:
(5 * 14 + 4 * 9)/(7 * 14 - 2 * 9) = 106/80 = 53/40

• Q19) If a shopkeeper wrongly calculates his profit on SP and gets 30% Loss, Find the actual Loss percentage.

• Play with fractions.
We have L/SP = 3/10
Hence, L/CP = 3/13 = 23.1 % (approx)

• Q20)There are three discount types that a shop offers:
Type 1: Buy 3 get 1 free
Type 2: Buy 2 get 50% off on 2nd one
Type 3: 30% flat off
Type 4: Buy 5 get 2 free
Which option offers the highest discount ?

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