BANK & INSURANCE (SBI PO MAINS 2025) MOCKTEST 2

First term of the series = 2000
Last term of the series = 2000
Third term of the series = 16000
Fourth term of the series = 16000

Let the second and fifth term of the series be X

Series: 2000, X, 16000, 16000, X, 2000

The pattern of the series:
2000, X = 8000, 16000, 16000, X = 8000, 2000

×4, ×2, ×1, ×0.5, ×0.25

8000 = X

Required answer = 8000/16000 = 1/2

Information Given in the Question:
25% of efficiency of A / 25% of efficiency of (B + C) = 1/1
Efficiency of A = Efficiency of B + C

Time taken by (A + B) to complete 50% work : Time taken by C to complete whole work
= 1 : 4

A + B + C together can complete the work in 3 days

Concept/Formula Used in the Question:
Work = Efficiency × Time

Efficiency is inversely proportional to time (more efficient = less time):
If total work = W, then time to complete = W / efficiency

If A + B + C complete work in 3 days → Total work = (A + B + C)’s efficiency × 3

Detailed Explanation:
Let efficiency of A = a

Since A = B + C → Efficiency of B + C = a
So total efficiency (A + B + C) = a + (B + C) = a + a = 2a

Let total work = LCM of days = 6a units
So if efficiency = 2a, then time to complete = 6a / 2a = 3 days

Now, from second condition:
Time taken by A + B to do 50% of work : Time taken by C to do full work = 1 : 4

Let efficiency of A + B = a + b
Efficiency of C = c = a − b (since A = B + C → C = A − B)

Now,
Time taken by A + B to do 50% of work = (0.5 × 6a) / (a + b)
Time taken by C to do full work = (6a) / (a − b)

Given their ratio = 1 : 4

(3a)/(a + b) : (6a)/(a − b) = 1 : 4

(3a/(a + b)) × ((a − b)/6a) = 1/4

(3(a − b)) / (6(a + b)) = 1/4

( (a − b) / (2(a + b)) ) = 1/4

2(a − b) = a + b

2a − 2b = a + b

a = 3b
So, A’s efficiency = a = 3b
Then, B = b
So, C = a − b = 3b − b = 2b

Now, A + B + C = 3b + b + 2b = 6b
Total work = 6a = 6 × 3b = 18b
Time taken by B alone = Total work / B’s efficiency = 18b / b = 18 days

The sum of A and P = 8
Difference between the A and P = 4
P > A
So, P = (8 + 4)/2 = 6
A = 2

2 B/C and 6 Q/R
C × R = 32

Possible values so C and R

Given, B > 2 and Q > 4
So, values of C and R is 4 and 8 respectively.

2 B/4 and 6 Q/8

The maximum possible fraction = 6 7/8

Q maximum value is 7
So, required answer = 6 7/8

Let products produced by A, B and C be P, Q and R respectively.

Given, P + Q = 59
And
Q + R = 48

For every 6 products sold by A, B sold 5 products.
For every 19 products sold by C, A sold 30 products.

Let the products sold by A be 30a
The products sold by B = 30a × 5/6 = 25a
The products sold by C = 19a

Also given,
30a + 25a + 19a = 74
a = 1

The products sold by A = 30
The products sold by B = 25
The products sold by C = 19

The product unsold by C = R − 19
The product unsold by B = Q − 25
The product unsold by A = P − 30

R − 19 = √(P − 30) + (Q − 25)

R − 19 = √(P + Q − 55)
R − 19 = √(59 − 55)
R − 19 = √4
R − 19 = 2
R = 21

Q + 21 = 48
Q = 27

P + 27 = 59
P = 32

Persons Products produced Products sold Products unsold
A  32  30  2
B  27  25  2
C  21  19  2

Required answer = 15 × 30 + 25 × 20 = 450 + 500 = 950

The average of the products produced by A, B, and C
= (32 + 27 + 21)/3 = 26.67

The production target for D = 27

I. The number of products sold by B = 25
The number of products unsold by B = 2
25 = 2²
25 ≠ 4 (incorrect)

II. The number of products produced by C < The number of products sold by B.
21 < 25 (correct)

III. The number of products produced by A > The number of products produced by B and C together.
32 > (25 + 19) 32 < 44 (incorrect)

Information Given in the Question:
Number of blue balls = X
Number of green balls = Y
Two balls are drawn without replacement

Basic Explanation:
First pick: blue = X/(X+Y)
Second pick: green = Y/(X+Y−1)

⇒ Probability = X/(X+Y) × Y/(X+Y−1)

OR

First pick: green = Y/(X+Y)
Second pick: blue = X/(X+Y−1)

⇒ Probability = Y/(X+Y) × X/(X+Y−1)

Required answer = X/(X+Y) × Y/(X+Y−1) + Y/(X+Y) × X/(X+Y−1)
= 2XY/(X+Y−1)(X+Y)

Information Given in the Question:
Volume of cylinder = x cm³
Initially 50% of the cylinder is filled with liquid → Volume = x/2 cm³

After inserting 1 sphere, liquid height rises by 2 cm
Then 4 more spheres are added → total of 5 spheres cause the cylinder to be completely filled

Volume of each sphere = y cm³

Concept/Formula Used in the Question:
Volume of liquid displaced = Volume of sphere submerged

If a submerged sphere raises the liquid by h cm, then:
Volume displaced = cross-sectional area of cylinder × h

Volume displaced by all 5 spheres = x/2 (as it goes from 50% to 100%)

Detailed Explanation:
Let the cross-sectional area of the cylinder = A cm²
When first sphere is dropped, the liquid level rises by 2 cm
Volume displaced = A × 2
This is equal to the volume of one sphere, i.e.,
A × 2 = y
A = y/2

When 5 spheres are added, total volume displaced = 5xy
But this volume fills the remaining 50% of the cylinder:
x/2 = 5y
x = 10y

Thus, the value of 50% of the volume of the cylinder is 5y
Let’s check each option by assuming x/2 = 5y

Option (a): 3/10 × volume of cylinder + 2 × volume of sphere
(3/10)x + 2y
x = 10y
3y + 2y = 5y

So, option (a) is correct.

The smallest prime number = 2
a = 2

Series P: 2, 2 + 2², 2(2) - 2, 3(2), 2, 3(2) + 2, 1.5(2) - 1

Series P: 2, 4, 2, 6, 2, 8, 2

The pattern of the series:
2, 4, 2, 6, 2, 8, 2

×2  +2  ×3  +3  ×4  +4

Fourth term of the series = 6