Maths & Logical Reasoning Test - 10 - SSC CGL MCQ

Given:

A contractor agreed to construct a road in 200 days and had 140 men to do such work.

Only 1/4 th of the road could be build after 60 days.

Formula used:

= (where, M is the number of men, D is the number of days, T is the time, W is the amount of work done.)

Calculations:

Amount of work remaining = 1 - (1/4) = (3/4) units of work.

Number of days in which the remaining work needs to be completed = 200 - 60 = 140 days.

Let x men be extra needed to finish the work.

=

3 × 60 = 140 + x

180 = 140 + x

x = 40.

∴ The answer is 40.

If we add both the figure then we get the new figure given below -

It is a parallelogram.

And we know that the area of parallelogram = (1/2) x h x (a + b)

Where h is the height and a, b is the length of the parallel sides of the parallelogram.

Now 2(a + b) = (1/2) x h x (2a + 2b + 2a + 2b)  

⇒ 2(a + b) = (1/2) x h x (4a + 4b) 

⇒ 2(a + b) = (1/2) x h x 4(a + b) 

⇒ h = 1

Hence the option (ii) is correct.

Given

sinα + sin²α = 1

Formula used:

⇒ sin² + cos² = 1 

Solution

As given,

⇒ sinα + sin²α = 1 ​

⇒ sinα = 1 - sin²α

⇒ sinα = cos²α  ...eq(1)

Now, in the given question:

​⇒​ 1 - cos²α - cos⁴α  

⇒ 1 - (cos²α + cos⁴α) ...eq(2)

Putting the value of eq 1 in eq 2.

⇒ 1 - (sinα + sin²α)  where 1 - (sinα​​​​​​​ + sin²α) 

⇒ 1 - 1 = 0​

The maximum capacity of each bowl is 11R3 /42 m3

So the total volume oil taken out is N x (11R3 /42) m3........................................................ (1)

Volume of the cylinder is (22/7) x R² x h = (22/7) x R2 x (R + 7)......................................... (2)

The volumes of N hemispherical bowls = N x (2/3) x (22/7) x r³......................................... (3)

Equating equations (1) and (2),

N x (11R3 /42) = (22/7) x R2 x (R + 7)

NR = 12R + 84

R x (N - 12) = 84

R = 84/(N - 12)..................................................................................... (4)

For R to be an integer value, N - 12 must be a factor of 84.

And both N and R are positive integers,

So,

N > 12.

And the values of R can be 0 < R < 85.

Checking the answers for all the given options:

For N = 13,

R = 84/(13 - 12) = 84.

Here we get R and N both as integers.

So, N = 13 is a possible value.

For N = 8 we get a negative value,

So it is not possible.

For N = 16,

R = 84/(16 - 12) = 21.

Here we get R and N both as integers.

So, N = 16 is a possible value.

For N = 17,

R = 84/(17 - 12) = Non-integer value.

So, the only possible solutions are N = 13 and N = 16.

Hence, the correct answer is 3.

Given:

Sujit bought an article for Rs. 6700.

He spent Rs. 2700 on it.

He marked the price 15% above his total cost price.

He allows two successive discounts of 5% on it.

Formula used:

Final Price = Marked Price × (1 - Discount1/100) × (1 - Discount2/100)

Calculation: 

Total cost price (CP) = Purchase price + Maintenance

= Rs. 6700 + Rs. 2700 = Rs. 9400

Marked Price (MP) = CP + 15% of CP

= Rs. 9400 + 0.15 × Rs. 9400

= Rs. 10810

Final Selling Price (SP) = MP × (1 - Discount1/100) × (1 - Discount2/100)

= Rs. 10810 ×(1 - 5/100) × (1 - 5/100)

= Rs. 10810 × 0.95 × 0.95

= Rs. 9756.025

Hence, the correct answer is that the selling price of the article is Rs. 9756.025

=Given:-

sinθ + cosθ = √2

Formula used:-

sin²θ + cos²θ = 1

2sinθ.cosθ = sin2θ

Calcualtion:-

Squaring both sides-

⇒ (sinθ + cosθ)² = 2

⇒ sin2θ + cos2θ + 2sinθ.cosθ = 2

⇒ 1 + 2sinθ.cosθ = 2

⇒ sin2θ = 1 = sin90

⇒ 2θ = 90

⇒ θ = 45^o

Given:

Amount = Rs. 7803, Rate = 4%, Time = 1 year.

Compounded half yearly.

Formula used:

Amount = principal[1 + (rate/100]^time

As compounded half yearly, rate becomes half and time becomes double.

Calculations:

Rate = 4%, becomes 4/2 = 2% and time = 1 year becomes 1 × 2 = 2year.

7803 = principal[1 + (2/100)]²

7803 = principal[1 + (1/50)]²

7803 = principal[51/50]²

7803 = principal × (2601/2500) 

Principle = = 7500

∴ The answer is Rs. 7500.

Calculation :

Number of degrees in 3(2/3) = 3(2/3) × 90° = 11/3 × 90° = 330°

∴ The correct answer is 330°.

3 Sin θ = 5 Cos θ


Divide by cos θ in both numerator and denominator


Hence, option B is correct.

Hence, Option C is correct.

Total number on a dice = 6
The prime number on a dice = 3 (2, 3 and 5)

Hence, Option B is correct.

Given:

17, 57, 22, 52, ?, 47

The logic followed in the given series:

Here, the missing term is '27'.

Hence, the correct answer is "Option (2)".

According to given coding language,

HOW = (total letters × 4) = 12

In the same way -

LION = (total letters × 4) = 16

Given : x z x _ y z x _ _ x y z x z _ _ y z

By checking options :

1. x z x y x → x z x x y z x z x x y z x z y x y z → (It doesn't Follows the pattern)
2. x z x x x → x z x x y z x z x x y z x z x x y z → (It follows the pattern of : x z x x y z - x z x x y z - x z x x y z)
3. x z y z x → x z x x y z x z y x y z x z z x y z → (It doesn't Follows the pattern)
4. x z x x y → x z x x y z x z x x y z x z x y y z → (It doesn't Follows the pattern)

⇒Option - (2) gives the pattern of "x z x x y z - x z x x y z - x z y x y z"

Hence, "x z x x x" is the correct answer.

The least possible Venn diagram is given below according to the given information.

Conclusion:

I. No T is A → Does not follow → (As some A are T and some T are H. So, no T is A is not definitely followed)

II. No H is T → Does not follow → (As some A are T and some T are H. So, no H is T is not definitely followed)

III. No A is H → Does not follow → (As some A are T and some T are H. So no A is H is not definitely followed)

So, Neither conclusion follows.

Hence, the correct answer is "Option 4".

Assertion (A): People and their problems are unique. → True

Reason (R): Active listening conveys something to the person who is listened to. → True

Here, (A) and (R) both are true but (R) is not the correct explanation of (A). This is because (R) does not explain why and how the people and their problems are unique.

Hence, option 1 is the correct answer.

The logic followed here is:

So, 'Brother' will be coded as 'Mn'.

Hence, the correct answer is "Option 4".

Here, we need to find the pattern and get the missing number.

The logic here is: (1st number × 3) + (1st number ÷ 3) = 2nd number.

1) 93 × 3 + 31 = 310,

2) 54 × 3 + 18 = 180

3) 48 × 3 + 16 = 160 ≠ 165

4) 33 × 3 + 11 = 110

Thus, the pattern is: Each 1st is multiplied by 3 and then 2nd term first two digits are added to the answer to get the final answer.

Hence, the correct option is 48 - 165

Alternate MethodLogic: (1st number ÷ 3) × 10 = 2nd number.

1) (93 ÷ 3) × 10 → 31 × 10 = 310,

2) (54 ÷ 3) × 10 → 18 × 10 = 180,

3) (48 ÷ 3) × 10 → 16 × 10 = 160 ≠ 165

4) (33 ÷ 3) × 10 → 11 × 10 = 110.

The logic here followed is:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic → The words are coded as the sum of the letter's positional values.

MALE: 13 + 1 + 12 + 5 = 31

FEMALE: 6 + 5 + 13 + 1 + 12 + 5 = 42

Similarly,

ADULT: 1 + 4 + 21 + 12 + 20 = 58

Hence, the correct answer is "58".

LOGIC: Two Figures of First Image Combine to give second Image.

In Figure (1) and Figure (2) →

Similarly;

In Figure (3) and Figure (4) →

Hence, the correct answer is "Option (3)".

Combining both statements:  U < M = I ≤ X < E ≥ P

Conclusion I: M > P

Here M < E ≥ P, hence no relation is possible. Thus conclusion I does not follows.

Conclusion II: U < E

Here U < X < E, hence U < E. Thus conclusion II follow.

Hence option C is correct.

Forward direction pairs –LS, ST
Backward direction pairs – EM, NO
Four pairs are there which have as many letters as they have between them in the English alphabetical series.
Hence, Option C is correct.

In the given Venn diagram d represents the people who pet cats and dogs but not rabbits.

Hence option B is correct.

19 $ 18 # 12 @ 42 % 14 =?
After changing the signs,
19 + 18 – 12 × 42 ÷ 14 = ?
or, 19 + 18 – 12 × 3 = ?
or, ? = 37 – 36 = 1
Hence, option A is correct.

Using the above information we get,

G > K > J > H > I

Clearly, G is the oldest person.
Hence, option A is correct.

Hence, option B is correct.

The given numbers are related as,
(23, 82, 484) → [(2 × 3) + (8 × 2)]² = [6 + 16]² = 22² = 484
Similarly, the option relates to the same number pair is,
(36, 52, 784) → [(3 × 6) + (5 × 2)]² = [18 + 10]² = 28² = 784
Hence, Option B is correct.

In order to believe into the argument of others it is best to build your own argument on the basis of evidence backed research. Thereby, in such scenario where one has to build consensus it is important to check with the effectiveness of the tool.
Hence, option C is the best answer.

Keeping patience in this scenario and managing time to help colleague is more fruitful and a win-win situation for both.
Thereby, option C is the correct answer.