Quant Boosters  Soumya Chakraborty  Set 3

2014 = 2 * 19 * 53
check for the highest power of largest prime, here 53
2014! contains 38 53's
so 2014!! = 1! 2! 3! ... 2014! will contain 53 (1 + 2 + 3 ... + 37) + 38 = 37297First thing that you need to understand is getting the highest power of a certain prime that a given factorial will be divisible by
Let's say what is the maximum power of 2 that will divide 50!
In order to solve that, we will successively divide 50 by 2, and keep collecting the quotients. The answer will be sum of all the quotients
50/2 = 25
25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1Thus answer is 25 + 12 + 6 + 3 + 1 = 47
Now, if we need to figure out the max power of a certain composite, we need to check for each prime in the composite ...
In a certain factorial, if we need to check the max power of 2015 = 5 * 13 * 31
we need to check for each primes. But, in any factorial the number of 31s cannot exceed the number of 13s and the number of 5s. Thus, the number 2015s will be determined by 31s. Thus, checking by 31 alone is sufficient
If the question says 2015!!
31! will have one 31, so will 32!, so will 33! ... till 61!
So each of these are giving 1 power each, in total 31*162! to 92!, we will get 2 powers of 31 each... in total 31*2
This will carry on till 31 * 30
Now, let us consider the numbers: 960! and (961)!
960/31 = 30961/31 = 31
31/31 = 1Thus, although 960! gives 30 powers of 31,
961! gives 31 + 1 = 32 powersThis happens because the first quotient will leave a quotient when divided by 31
Again we will have this series: 31 * 32, 31 * 33, ... till the first quotient leaves a quotient of 1
62/31 = 2
But 61/31= 1thus 31 * 32, 31 * 33, ... 31 * 62
Extending this logic ... we get the answer

Q6) The MRP of a chocolate is Rs 65. A customer purchased the chocolate for 56 Rupees 16 Paise. He got two successive discounts of which one is 10%. Find the other discount of the discount scheme that was given by the seller.

Observe that both 65 and 56.16 are multiples of 13
dividing both by 13, we have 5 and 4.32
reduce 10% of 5 => you get 4.5
4.5 to 4.32 is a reduction of .18
which is 4%

Q7) If all the sides of a cuboid increases by 8%, its volume increases by x%
If all the sides of a different cuboid reduces by 8%, its volume reduces by y%
Which of the following is true?
a) x = y
b) x > y
c) x < y
d) We need the initial side ratio of the two cuboids that we begin with

Understand this LOGICALLY
when we have successive change over +a and +a, the net change will be more than 2a
when we have successive change over a and a, the net change will be less than 2a
Think over the successive change formula, you'd understand
So, the x% must be greater than y%

Q8) A grocer sells a soap markerd Rs 30 at 15% discount and gives a shampoo sachet costin Rs 1.5 free with each soap. He then makes 20% profit. His cost price per soap is

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

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?

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%

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.

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.