ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: 5 ÷ √5 = ?

Solution:
5 ÷ √5
= 5/√5
= √5

Question: If n is a positive integer, which of the following must be even?

Solution:
Since n is an integer, it can be EVEN or ODD.
But any integer when multiplied by 2 is even.
For example, 3 × 2 = 6 (even)

The rule is:
EVEN × ODD = EVEN
EVEN × EVEN = EVEN
ODD × ODD = ODD

A) we cant say as it depends if n is odd or even

B) same as (A)

C) Even as n is multiplied by 2

D) It is ODD as EVEN+1 = ODD

E) depends if n is even or odd.

Question: 37.5% of 800 - 6.25% of 1600 =?

Solution:
37.5% of 800 - 6.25% of 1600
= (375/1000) × 800 - (625/10000) × 1600
= 300 - 100
= 200

Question: Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 ≤ 5?

Solution:
x + 6 > 10
⇒ x > 4

x - 3 ≤ 5
⇒ x ≤ 8

Bringing these two inequalities together we get:
4 < x ≤ 8

Question: (√289/34) × (68/√1156) × (√961/62) =?

Solution:
(√289/34) × (68/√1156) × (√961/62)
= (17/34) × (68/34) × (31/62)
= 1/2

Question: What is 45 percent of (7/12) of 240?

Solution:
Here 7/12 of 240 is (7/12) × 240 = 7 × 20 = 140

Now 45 Percent of 140 we have to find out.
45% of 240 = (45/100) × 140 = 63.

Question: If the sum of 5, 8, 12, and 15 is equal to the sum of 3, 4, x, and x + 3, what is the value of x?

Solution:
5+8+12+15 = 40

Now,
40 = 3 + 4 + x + x + 3
⇒ 40 = 10 + 2x
⇒ 30 = 2x
⇒ 30/2 = x
∴ 15 = x

Question: 1 - [2 - {3 - (4 - 5) + 6} + 7] =?

Solution:
1 - [2 - {3 - (4 - 5) + 6} + 7]
= 1 - [2 - {3 - (-1) + 6} + 7]
= 1 - [2 - {3 + 1 + 6} + 7]
= 1 - [2 - {10} + 7]
= 1 - [2 - 10 + 7]
= 1- [-1]
= 1 + 1
= 2

Question: W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X - 7, what is the sum of all possible values of W?

Solution:
From the given information, we can write: X = YZ + W
Also given: W = X - 7

X = YZ + W
⇒ X = YZ + X - 7
⇒ 0 = YZ - 7
∴ 7 = YZ

There are only 2 possible cases:
case 1: Y = 1 and Z = 7
case 2: Y = 7 and Z = 1

case 1 yields a CONTRADICTION.
If Y = 1, then we are dividing X by 1, and if we divide by 1, the remainder will always be ZERO.
In other words, if Y = 1, then W = 0 So, we can definitely rule out case 1,

It must be the case that Y = 7 and Z = 1 (case 2)

So, we have: When X is divided by 7, the quotient is 1 and the remainder is W
This tells us that 7 divides into X 1 time
So, the possible values of X are: 7, 8, 9, 10, 11, 12 and 13 (since 7 divides into each value 1 time.

Let's check each case.
If X = 7,
then the remainder (W) is 0. 
Doesn't follow the rule.

If X = 8,
then the remainder (W) is 1.
Since Y = W,
Doesn't follow the rule.

If X = 9,
then the remainder (W) is 2.
So, when X (9) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 2.
Follows the rule.

If X = 10,
then the remainder (W) is 3.
So, when X (10) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 3.
Follows the rule.

If X = 11,
then the remainder (W) is 4.
So, when X (11) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 4.
Follows the rule.

If X = 12,
then the remainder (W) is 5.
So, when X (12) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 5.
Follows the rule.

If X = 13,
then the remainder (W) is 6.
So, when X (13) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 6.
Follows the rule.


Sum = 2 + 3 + 4 + 5 + 6
= 20

Question: The number 2 - 0.5 is how many times the number 1 - 0.5?

Solution:
Let,
2 - 0.5 is x times the number 1 - 0.5

So,
(2 - 0.5) = x × (1 - 0.5)
⇒ 1.5 = x × 0.5
⇒ x = 1.5/0.5
∴ x = 3

Question: If x is a positive integer and 4^x - 3 = y, which of the following CANNOT be a value of y?

Solution:
If x = 1:
4¹ - 3 = 1

If x = 2:
4² - 3 = 13

If x = 3:
4³ - 3 = 61

The only value that y cannot take is 7.

Question: When 35 - [30 - {35 - (15 - *)}] = 60, then * is equal to-

Solution:
35 - [30 - {35 - (15 - *)}] = 60
⇒ 35 - [30 - {35 -15 +*}] = 60
⇒ 35 - [30 - {20 + *}] = 60
⇒ 35 - [30 - 20 - *] = 60
⇒ 35 - [10 - *] = 60
⇒ 35 - 10 + * = 60
⇒ 25 + * = 60
∴ * = 60 - 25 = 35