২২১৬১
A room contains 200 people, 25% of whom are graduates. A group of people, 30% of whom are graduates, leave the room. Of the remaining people, 10% are graduates. How many people did leave the room?
উত্তর
150
সমাধান
Let the number of people leaving be L.
Remaining people = 200 - L
Total graduates = 25% of 200 = 50
Leaving graduates = 30% of L = 0.3L
Remaining graduates = 50 - 0.3L
ATQ, 10% of (200 - L) = 50 - 0.3L
or, 20 - 0.1L = 50 - 0.3L
or, 0.3L - 0.1L = 50 - 20
or, 0.2L = 30
or, L = 30 / 0.2 = 150
২২১৬২
How many tiles, each a square tile of 2 inch sides, are needed to cover a rectangle floor of 4 feet long and 6 feet wide?
উত্তর
864
সমাধান
Measurements of the floor are 4 feet or 48 inches and 6 feet or 72 inches.
So, area of the floor = 48 x 72 = 3456 sq in
Area of each tiles = 2 x 2 = 4 sq in
Number of tiles needed = 3456/4 = 864
২২১৬৩
There are three different roads from Shah Bag to Farm Gate and 4 different roads from Farm Gate to Banani. How many different routes are there from Shah Bag to Banani via Farm Gate?
উত্তর
12
সমাধান
At the end of each different road from Shahbag to Farmgate, there is 4 different ways to go to Banani. So, total number of routes from Shahbag to Banani is 3 x 4 = 12.
২২১৬৪
You are to arrange 36 identical chairs in rows such that there is same number of chairs in each row. Each row must contain at least 4 chairs and there must be at least 3 rows. How many different arrangements are possible?
উত্তর
5
সমাধান
4 chairs in 9 rows = 36 chairs
6 chairs in 6 rows = 36 chairs
9 chairs in 4 rows = 36 chairs
12 chairs in 3 rows = 36 chairs
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
So, total ways = 4
২২১৬৫
The probability that a student will graduate with honors and get a good job is 0.09 whereas the probability that a student will graduate with honors is 0.1. What is the probability that a student will get a good job if she graduates with honors?
উত্তর
90%
সমাধান
Probability of graduating with honors, P(H) = 0.1
Probability of graduating with honors and getting a good job, P(H∩J) = 0.09
Probability of getting a good job if she graduates with honor, P(J/H) = P(H∩J)/P(H) x 100% = 0.09/0.1 x 100 = 90%
২২১৬৬
A South American visitor was confused to read that the next day's temperature would be 77 degree Fahrenheit. Translate that into Celsius for him with this formula C = 5/9 *F-32?
উত্তর
25
সমাধান
Temperature in Fahrenheit, F = 77°F
Temperature in °C = 5/9 x (F - 32) = 5/9 x (77 - 32) = 25°C
২২১৬৭
If (x+3y)=15 and x=-1.5y, then x=?
উত্তর
-15
সমাধান
Here. x = - 1.5y
or, x = - 3y/2
or, y = - 2x/3
Now, x + 3y = 15
or, x + 3( - 2x/3) = 15
or, x - 2x = 15
or, - x = 15
SO, x = - 15
২২১৬৮
If n is an even integer which of the following must be an odd integer?
উত্তর
3(n+1)
সমাধান
If n is an even integer then n + 1 must be an odd integer. Product of two odd integers is always an odd number. So, 3(n + 1) must be an odd number.
২২১৬৯
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
উত্তর
8
সমাধান
Two offices can be filled in two ways, when all the three employee will be in same room or when two employee in one room and one in other room.
when all the three employee will be in same = 3C3 * 2! = 2 (2!, because any of the room can be taken)
when two employee in one room and one in other room. = 3C2 * 1C1 * 2! = 6
Hence total ways = 6 + 2
Answer is 8.
২২১৭০
How much salt must we add to 10 grams of a 20% salt solution to strengthen it into a 50% solution?
উত্তর
6 gm
সমাধান
Let the amount need to be added be x grams.
So, x + 20% of 10 = 50% of (10 + x)
or, x + 2 = 5 + 0.5x
or, x - 0.5x = 5 - 2
or, 0.5x = 3
So, x = 6 grams