# Quant Boosters by Hemant Malhotra - Set 12

• Sum of two or more consecutive positive integers is 100. How many such sets are possible?

Let number starts from a
so a+(a+1)+.....(a+(n-1)*d))=100
so n/2 * (2a+(n-1) * d))=100
so n(a+(n-1)/2))=100
so (n-1)/2 should be integer so n should be odd
so n will be odd factors of 100
and odd factors of 100=3
but n=1 is not allowed min terms =2 given
so 3-1= 2

How many ordered pairs (a, b, c) exist such that their LCM is 400?

LCM=2^4 * 5^2
LCM(a, b, c)=2^4 * 5^2
check if we want to find lcm of 2^2 and 2^3 LCM will be 2^3 , if 2^3 and 2^3 still LCM=2^3
so we will pick higher power and that should be in at least one of the number
so at least one=total-none
now for 2^4 , a have 2^0,2^1... 2^4 so 5 choices
same for b and c
so 5 * 5 * 5 = 5^3 choices
now when none have highest power then a, b, c have 4 choices
so 5^3-4^3
same for 5^2
a have 3 choices , same for b and c so 3^3
and when none have highest then all have 2 choices so 3^3-2^3
so (5^3-4^3) * (3^3-2^3)

Saral and Abhishek start simultaneously from a point on a circular track in the same direction at uniform speeds of 'x' km/hr and 'y' km/hr respectively. They meet for the first time when Saral is in his third round. Which of the following cannot be the value of x : y?
(1) 11:7
(2) 9:5
(3) 11:5
(4) 13:7

Speed of saral=x
speed of abhishek=y
let track length=D
and they met at a distance of d first time
so x/y = (2D+d)/D+d
because x/y=1+((D/(D+d))
now 1/2 < D/(D+d) < 1
so 3/2 < x/y < 2
so speed ratio should be in between 3/2 to 2
and 11/5 is greater than 2 so 11/4 can't be the value so OA= 3

I am 7 times as old as you were when I was as old as you are", said a man to his son. Find their present ages if the sum of their ages is 110 years.

x = 7(y -(x-y))
x = 7(2y -x)
8x = 14y or 4x = 7y
x + 4x/7 = 110
11x/7 = 110
x = 70 , y = 40

Find the difference between S.I and C.I on 2000 for 3 years at the rate of 10% per annum.

For three years, Direct formula: Difference = P[(R/100)^3 +3(R/100)^2]

If A is twice more efficient as B, B is thrice more efficient as C, C is twice more efficient than D then what is the ratio A:B:C:D?

Let D = x
so C is twice more means C = x + 2x = 3x
and B is thrice more so 3 * 3x + 3x = 12x
and A will be Twice more =12 * 3 = 36x
so 36:12:3:1

Three athletes A, B and C run a race, B finished 24 meters ahead of C and 36 m ahead of A, while C finished 16 m ahead of A. If each athlete runs the entire distance at their respective constant speeds, what is the length of the race?

Initial gap is 4 then distance is 24,
For gap 16, d =24*4= 96

Running at a uniform speed in a race, A can beat B by 20 m, B can beat C by 10 m, and A can beat C by 28 m. How long is the race?

When A reaches the end point of race B is 20 m behind and C is 28 m behind so gap b/w B and C is 8 m . Now if B has to reach end point it needs to cover 20m and in this 20 m it is creating additional gap with C as 10-8 = 2 m so in 20 m it creates 2m gap. Hence in how many m it will create 10 m gap will be : 20*10/2 = 100

The breadth of a rectangle decreases by 33.33%. By what percent should the length be increased so as to maintain the same area?

Decrease of 33.33% means 1/3 means 3 becomes 2 so 2 will become 3
which means an increase of 50%

Trumph at the time of selling and purchasing, weighs 10% less and 20% more per kilogram respectively. Find the percentage profit earned by Trumph (Assuming he sells at Cost Price)

Method1- Let's say original weight is 100 now he is taking 20% extra so total 120 and selling 10% less so 90. So (120-90/90) * 100 = 30/90 * 100= 33.33%
Method2- multiplying factor
1 * 10/9 * 6/5 = 1.33 so 33%

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