MATH SOLUTION
Rupali Bank Limited - Officer
Exam of 08-Nov-2019
Solved by: Sultan Mahmud Cxlvii
1. If both x and y are prime numbers, which of the following CANNOT be the product of x and y? (6 / 10 / 35 / 27)
=>
6 = 3×2 [both are prime]
10 = 5×2 [both are prime]
35 = 7×5 [both are prime]
27 = 27×1 = 9×3 [at least one of them must be non-prime]
ans: 27.
2. How many integers from 1 to 1000 are divisible by 30 but not by 16?
=>
Number of integers from 1 to 1000 that are divisible by 30 = (1000÷30) = 33
LCM of 30 and 16 = 240
Number of integers from 1 to 1000 that are divisible by 30 and 16 (i.e: 240) = (1000÷240) = 4
So, the number of integers from 1 to 1000 that are divisible by 30 but not by 16 is = 33-4 = 29.
ans: 29.
3. P and Q are brothers. R and S are sisters. The son of P is brother of S. Q is related to R as-
=>
According to the question,
R and S are the daughters of P.
So, Q is the uncle of R.
ans: uncle.
4. If w is 10% less than x and y is 30% less than z, then wy is what percent less than xz?
=>
w = (100-10)% of x = 0.9x
y = (100-30)% of z = 0.7z
wy = 0.9x × 0.7z = 0.63xz = (100-37)% of xz
So, wy is 37% less than xz.
ans: 37%
5. Every 3 minutes, 4 liters of water are poured into a 2,000 litre tank. After 2 hours, what percent of the tank is full?
=>
Total water poured in 2 hours = (2×60/3) × 4 = 160
Required percentage = 160/2000 = 8%.
ans: 8%.
6. The next number in the sequence 3, 6, 11, 18, 27, ... is-
=>
The differences between two consecutive terms:
3, 5, 7, 9 ....
so, the next difference should be 11.
so, the next number in the sequence is 27+11 = 38.
ans: 38
7. The HCF of two numbers is 24. The number which can be their LCM is- (84 / 128 / 148 / 120)
=>
Suppose, the numbers are 24x and 24y where x and y are coprime numbers.
So, their HCF = 24
their LCM = 24xy
Here, whatever be the value of x and y, we can say, their LCM is a multiple of 24.
Among the option values only 120 is a multiple of 24. So, 120 can be the LCM of the given numbers.
ans: 120.
8. The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is-
=>
Sum of the remaining two numbers = (sum of eight numbers) - (sum of six numbers) = 14×8 - 16×6 = 16
Average of those two numbers = 16÷2 = 8.
ans: 8
9. If A = {1,2,3,4,5}, then the number of proper subsets of A is-
=>
Number of elements of A = 5
Number of proper subsets of A = 2^5 - 1 = 31.
ans: 31
10. Two numbers are in the ratio 2:5. If 16 is added to both the numbers, their ratio becomes 1:2. The numbers are-
=>
Suppose, the numbers are 2x and 5x respectively.
According to the question,
(2x+16) : (5x+16) = 1 : 2
5x + 16 = 4x + 32
x = 16
The numbers are = 2×16 = 32 and 5×16 = 80.
ans: 32,80.
11. If 1-2x ≤ 3 then-
=>
1 - 2x ≤ 3
-2x ≤ 3-1
-2x ≤ 2
2x ≥ -2
x ≥ -1.
ans: x ≥ -1
12. If y/x = 1/3 and x + 2y = 10, then x is-
=>
given,
y/x = 1/3
y = x/3
again,
x+2y = 10
x + 2x/3 = 10
5x = 30
x = 6
ans: 6.
13. How many real roots does the polynomial 2x³+8x-7 have?
=>
Theorem: The polynomial ax³+bx+c will have exactly one real root if both 'a' and 'b' have values greater than zero.
Here, a = 2, b = 8, both are greater than zero. So, the polynomial has only one real root.
ans: one.
14. If xy = 2 and xy² = 8, what is the value of x?
=>
xy² ÷ xy = 8÷2
or, y = 4
so, x = 2/4 = 1/2.
ans: 1/2.
15. If a - 1/a = 2, what is a³ - 1/a³?
=>
Given, a - 1/a = 2
or, (a - 1/a)³ = 2³
or, a³ - 1/a³ - 3.a.1/a.(a - 1/a) = 8
or, a³ - 1/a³ - 3×2 = 8
or, a³ - 1/a³ = 14.
ans: 14.
16. The tree sides of a triangle are x+1, 2x-1 and 2x+1 respectively and the perimeter is 26 cm. The length of the smallest side is ---
=>
Given,
x+1 + 2x-1 + 2x+1 = 26
5x = 25
x = 5
Lengths of the sides: 5+1 = 6, 2×5-1 = 9, 2×5+1 = 11.
Length of the smallest side = 6.
ans: 6 cm.
17. There are 10 true-false questions in an examination. These questions can be answered in-
=>
Number of options = 2
Number of questions = 10
Number of ways to answer = 2^10 = 1024.
ans: 2^10 or 1024 ways.
18. If two fair coins are flipped, what is the probability that one will come up heads and the other tails?
=>
Possible outcomes = {HH, HT, TH, TT}
Probability = 2/4 = 1/2.
ans: 1/2.
19. If the diagonal of a square measures 16√2 cm, what is the area of the square in sq.cm? =>
Properties of a square:
Length of a side = a
Length of the diagonal = a√2
Area = a²
Here, a√2 = 16√2 cm
so, a = 16 cm
so, a² = 16² sq.cm = 256 sq.cm.
ans: 256.
20. If Logx 9/16 = -1/2, then the value of the base is-
=>
Given,
Logx 9/16 = -1/2
or, x^(-1/2) = 9/16
or, 1/√x = 9/16
or, √x = 16/9
or, x = 256/81
ans: 256/81.
21. If cos A + cos² A = 1, then the value of the expression (cos² A + cos A) is-
=>
Given,
cos A + cos² A = 1
so, cos² A + cos A = 1.
ans: 1.
22. The difference in taka between simple and compound interest at 5% annually on a sum of Tk. 5000 after 2 years is-
=>
Simple interest = 5000 × 2 × 5% = Tk. 500
Compound interest = (5000 × 1.05²) - 5000 = 5000×105×105/100×100 - 5000 = Tk. 512.50
Difference = Tk. (512.50-500) = Tk. 12.50.
ans: 12.5
23. For y = -2x-8, what is the least value of x for which y is less than 9?
=>
y < 9
or, -2x - 8 < 9
or, -2x < 17
or x > -17/2
or, x > -8.5
So, the least value of x for which y is less than 9 is -8.
ans: -8.
24. A group of 7 members having a majority of boys is to be formed out of 7 boys and 4 girls. The number of ways the group can be formed is-
=>
Possible formations: 6 boys and 1 girl, 5 boys and girls, and 4 boys and 3 girls.
Number of ways = (7C6 × 4C1) + (7C5 × 4C2) + (7C4 × 4C3) = 7×4 + 21×6 + 35×4 = 28+126+140 = 294