# Discussion Room : Quant

• Find the number of number between 100 to 400 which are divisible. by either 2,3,5,7

• @deepalis727
According to me
numbers divisible only by 2 i.e 100 102 104 ... 400
numbers divisible only by 3 Now we are left with only odd numbers i.e 101 103 105 ... 399 we'll check for only multiples of 3 here, because even multiples of 3 have been taken cared by 2 the numbers will be 105 111 ... 399
numbers divisible only by 5 The numbers left will be 101 103 107 109 113 115 ... 395 We'll check for only multiples of 5 115 125 ... 395
numbers divisible only by 7 Now the numbers left we'll be 101 103 ... 397 And once again we'll check for only multiples of 7
The sum of multiples individually checked in 1, 2, 3, and 4 will give the answer

• @zabeer • @deepalis727
there are 299 numbers between 100 and 400 (excluding 100 and 400)
Out of 299 numbers [299/2] = 149 numbers are divisible by 2
Out of remaining 150 numbers [150/3] = 50 numbers are divisible by 3
Out of remaining 100 numbers [100/5] = 20 numbers are divisible by 5
Out of remaining 80 numbers [80/7] = 11 numbers are divisible by 7
so 149 + 50 + 20 + 11 = 230 numbers are divisible by 2, 3, 5 or 7
If it is including 100 and 400, then we have 232 numbers which are divisible by 2, 3, 5 or 7

• @vinaycat2017
Let the total distance be d
truck started it journey with 100 kmph and continued so for distance d/3
At d/3 it unloaded 150 cartons, so speed is increased by 20 + 20 + 400/100 = 44% (using successive percentage change formula)
So d/3 distance covered at 100 kmph
next d/3 distance covered at 144 kmph
and last d/3 distance covered at 172 kmph
average speed = 3abc/(ab + bc + ca) = 132 (approx)
d = 132 * 9.82 = 1296 km (approx)

• @zabeer
Two trains start simultaneously from A and B towards B and A respectively at 8 a.m. They cross each other at 12 noon. Train starting from B, thereafter, takes 6 hrs to reach A. On a particular day the train starting from A, reduced its speed and arrived at B, 200 min late. At what time did the trains cross each other on that day?
A)1:00 pm
B)2:00 pm
C)1:30 pm
D) None of these

• @zabeer • @zabeer
Find the volume of the solid obtained when the region bounded by y = √x, y = −x and the line x = 9 is revolved around the x-axis.

Sir, according to me that will be a cone having radius=6 unit and height=9 unit. So the required volume will be 108π. But tell me the right approach....

• @zabeer • @zabeer

A steel container is sold at Rs 120 cash or Rs 25 as cash down payment and Rs.25 a month for 4 months .The rate of interest per annum charged under the installment plan is .
(a) 26.09%
(b) 24.09%
(c) 20 %
(d) 23.25%

Sir i have tried this way. Worth of Rs 95 after 4 months = 25 * [100 * 4+(R * 4 * 3)/100]

Please guide me

• @zabeer
A,B and C start running along the circumference of a circle(circumference=1200 m) at the same time from the same point.A and B run in the clockwise direction with constant speeds of 8 m/s and 6 m/s respectively.C runs in the anticlockwise direction with a constant speed of 5 m/s.What is the time difference between the first two instances when C is equidistant from A and B along the circumference?
a)120 seconds b) 50 secs c)60 secs d) 100 secs
What's the procedure to solve this question?

• @vinaycat2017

120 rupees is the original price
25 rupees down payment means 95 rupees is what we are "Borrowing" from the shop.
Amount paid in instalments = 25 * 4 = 100
So 100 - 95 = 5 is the interest
Now this interest gained (Rs 5) is through the interest gained in the available amount month by month.
5 = 95R/(12 * 100) + 70R/(12 * 100) + 45R/(12 * 100) + 20R/(12 * 100)
5 = 230R/(12 * 100)
R = 6000/230 = 26.09%

• Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take 8/3 more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs, 450, then in how many days did A, B and C together complete the whole work?

• @vinaycat2017 Answer is 30 square units

• In how many ways can distinct words of 5 letters each be made using the English alphabet?

• @zabeer
A sphere passes through the midpoints of the twelve edges of a cube that has edges of length 6 inches. What is the surface area of the sphere, in square inches? Express your answer in terms of pi.

• What is the remainder when 13^66 – 23 is divided by 183?

• @zabeer • Usain is an athlete. While running, the number of calories burnt by him is directly proportional to the square root of his speed. If he runs 10 km at a constant speed of 25 km/hr, the total number of calories burnt is equal to 2400. On a particular day he ran at a constant speed of 36 km/hr and burnt 1800 calories. What was the distance run by him on that day? (Assume that calories burned are directly proportional to the distance travelled)

Can anybody help.

• @deepalis727
Given : No. of calories ∝ dist × √ (Speed)
so we can say that No. of calories burnt = K×dist×√ (Speed)
2400=K×10×5, Here k comes out to be "48".
Now, 1800=Dist×48×6
Dist=6.25 Km

3

6

8

1