Maths & Logical Reasoning Test - 7 - SSC CGL MCQ

Given:

Formula Used:

cos(90° – θ) = sin θ

cot(90° – θ) = tan θ

tan θ = (sin θ)/(Cos θ)

Calculation:

⇒ (Cos θ)(Cos θ)

⇒ Cos2 θ

∴ The value of is Cos² θ

Given:

Sidhu leaves his home at 03:20 PM.

Sidhu takes a taxi and arrives at the railway station 20 minutes after the scheduled train time.

Sidhu's friend arrives at the railway station at 05:20 PM, which is 10 minutes before the scheduled train time.

Formula Used:

Scheduled Train Time = Friend's Arrival Time + 10 minutes

Sidhu's Arrival Time = Scheduled Train Time + 20 minutes

Time Difference between Sidhu's and Friend's Arrival = Sidhu's Arrival Time - Friend's Arrival Time

Calculation:

⇒ Scheduled Train Time = 05:20 PM + 10 minutes = 05:30 PM

⇒ Sidhu's Arrival Time = 05:30 PM + 20 minutes = 05:50 PM

⇒ Time Difference = 05:50 PM - 05:20 PM = 30 minutes

∴ Sidhu arrived at the railway station 30 minutes after his friend.

Shortcut Trick
MP = (80 / 20%) × 100% = Rs 400

CP of book = 400 - 80 = Rs 320

∴ The correct answer is Rs. 320.

Alternate Method
Given:

Discount = 20%

SP of a Pen = Rs.80

Calculation:

Let MRP of a book be Rs.x

According to the question,

20% of x = 80

⇒ x = (80/20) × 100

⇒ x = Rs.400

He will pay for book = 400 - 80 = Rs.320

∴ The correct answer is Rs. 320.

Given:

The time is taken by boat upstream = 2(2/3)  hours

Formula used:

S = D/T

Where, S = Speed, D = Distance, and T = Time

Calculation:

Let the speed of the boat and speed of the current be 13s and 3s respectively,

The distance be D and the time taken in return journey be T

The upstream speed = 13s - 3s = 10s

The downstream speed = 13s + 3s = 16s

According to the question

2(2/3) = D/(10s) ----(1)

T = D/(16s) ----(2)

By equations (1) and (2)

⇒ (2(2/3)) × 10s = T × 16s

⇒ (8/3) × 10 = 16T

⇒ T = 5/3

The time is taken in return journey = 1(2/3) hours

∴ The required result will be 1(2/3).

Given:

Concept used:

Sin²θ + Cos²θ = 1

Calculation:

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒ 2 tan2 2α

∴ The required answer is 2 tan2 2α.

Given:

Concept used:

Calculation:

Putting A = 90°

On doing rationalization of second term, we get

⇒

⇒

⇒

⇒

⇒ (2√2 + 3)5 - (2√2 + 3)⁵

⇒ 0

∴ The required answer is 0.
Additional Information

Here, we can put any standard value of A from 0° to 90° as the given options are real values

And in the question part, we have not given any conditions for angle A.

Concept -

The formula for the volume of a right circular cylinder is V = πr²h, where r is the radius of the base and h is the height.

Explanation -

If the radius of the base is halved, the new volume V' of the cylinder with the halved radius becomes:

Now, let's find the ratio of the volume of the reduced cylinder to the volume of the original cylinder:

Ratio =

Therefore, if the radius of the base of a right circular cylinder is halved while keeping the height constant, the ratio of the volume of the reduced cylinder to the volume of the original cylinder is 1/4.

Hence the ratio of the volume of the reduced cylinder to the volume of the original cylinder is 1:4.

Given:

The diameter of a circular garden is 28 m.

Concept used:

Circumference of a circle = 2πr

Calculation:

Radius = 28/2 = 14 m

The fencing cover the distance 2 × π × 14 = 88 m

So, total cost of fencing 300 × 88 = Rs.26400

∴ The correct answer is Rs.26400

Given:

Time is taken by the train to cross the signal = 39 seconds

Time is taken by the train to cross the bridge = 82 seconds

Length of the bridge = 473 meters

Formula Used:

Length of the train = (Time taken to cross the bridge - Time taken to cross the signal) × Speed of the train

Calculation:

Let's assume that the speed of the train is 'v' (in meters/second). Then, we can set the equation:

v = Length of the train / Time taken to cross the signal

Substituting the value of 'v' in the second equation, we get:

v = Length of the train / Time taken to cross the signal

= Length of the train/39

Using the value of 'v' in the first equation, we get:

473 = (82 - 39) × Length of the train / 39

473 × 39 = (82 - 39) × Length of the train

18447 = 43 × Length of the train

Length of the train = 18447/43

Length of the train = 429 meters

Hence, the length of the train is 429 meters.

Given:

Selling price of the item = Rs 1,596

Profit = 14%

Formula Used:

Calculation:

Let the selling price be SP and the cost price be CP.

⇒ SP = CP + 0.14 × CP

⇒ SP = 1.14 × CP

⇒ CP = 1596/1.14

⇒ CP = 1400

Half of CP = 1400/2

⇒ Rs 700

∴ The half of the purchase price of that item is equal to Rs 700.

Concept:

Calculation:

Given

cos(π + θ) = ?

∵
∴ cos(π + θ) = - cosθ

PD × PC = PB × PA
PC × 4.5 = 7.7(7.7 + 3.1)
PC = 18.48 cm
CD = 18.48 – PD = 18.48 – 4.5 = 13.98 cm
Hence, option C is correct.

= 209.25
Hence, option C is correct.

Hence, Option A is correct.

Hence, Option B is correct.

The pattern followed here is,

Hence, the correct answer is "36".

Decoding the information,

Given:

58 - 9 + 18 ÷ 16 × 27 + 2 = ?

After replacing the signs from left to right and using the BODMAS rule,

= 58 ÷ 9 × 18 + 16 - 27 × 2

= 116 + 16 - 54

= 132 - 54

= 78

Hence, “78” is the correct answer.

By using the symbols in the table given below, we can draw the following family tree:

Let's check each option one by one.

Option 1) O % N $ P + S × W

⇒ O is the mother of N, N is the wife of P, P is the father of S, and S is the sister of W.

Clearly, here P is the father of W.

Option 2) O + W $ P + S × N

⇒ O is the father of W, W is the wife of P, P is the father of S, and S is the Sister of N.

Here, P is the husband of W.

Option 3) W ÷ S + P % N % O

⇒ W is the son of S, S is the father of P, P is the mother of N, and N is the mother of O.

Clearly, P is the sister of W.

Option 4) P + O $ N + W × S

⇒ P is the father of O, O is the sister of N, N is the father of W, and W is the sister of S.

Here, P is the Grandfather of W.

Hence, the correct answer is "Option 1".

The embedded part of this image is:

Hence, option (2) is the correct answer.

The logic followed here is:

Logic: The second word signifies the field in which the first person was awarded the Nobel Prize.

Here,

Rabindranath Tagore : Literature → Rabindranath Tagore was awarded the Nobel Prize in Literature.

Similarly,

Mother Teresa : ? → Mother Teresa was awarded the Nobel Prize in Peace.

Hence, the correct answer is "Peace".

By using the symbols in the table given below, we can draw the following family tree:

Given:- P @ Q # R % S @ T * U

⇒ P is the brother of Q, Q is the sister of R, R is the daughter of S, S is the brother of T, and T is the wife of U.

1) U is the Paternal Uncle of Q → Yes, U is the paternal uncle of Q. (Correct)

2) P is the son of S → Yes, P is the son of S. (Correct)

3) U is the wife of T → No, U is the husband of T. (Incorrect)

4) S is the father of Q → Yes, S is the father of Q. (Correct)

Hence, the correct answer is "Option 3".

The logic follows here is :-

1) XVRL

2) KIEA

3) RPLF

4) MKGA

∴ Here, 'KIEA' is different from other three alternatives.

Hence, the correct answer is "KIEA".

Preparing the family tree using the following symbols:

i) Reena is the sister of Abhi.

ii) Ajay is the brother-in-law of Abhi.

iii) Picku is the daughter of Ajay.

iv) Ramesh is the father of Reena.

v) Abhi is the son of Ramesh.

A possible tree diagram will be:

Therefore, Ramesh is the Grandfather of Picku.

Hence, the correct answer is "Grandfather".

When the folder paper is opened, the cuts will appear as follows:

Hence, option 3) is the correct answer.

Conclusions:

I. Only candidates with an MBA degree in marketing can apply.

The statement states that 7 or above years of experience in marketing is required but nothing is mentioned about the requirement of degree for the post. Thus, conclusion I doesn't follow.

II. Applications of candidates with 6 years of experience in marketing will not be considered for the post.

It is cleared from the statement that candidates who do not have 7 or above years of experience will not be considered for the post. Thus, conclusion II follows.

Hence, only conclusion II follows.

(81, 17) → (8 × 1) + (8 + 1) = 17
(65, 41) → (6 × 5) + (6 + 5) = 41
(47, 39) → (4 × 7) + (4 + 7) = 39
(53, 33) → (5 × 3) + (5 + 3) = 23
Hence, Option D is correct.

Hence, Option C is correct.

Using the above information, we get the following arrangement:

We get “D” is sitting immediate left of G.
Hence, Option A is correct.

Thus, P is the father- in- law of 'D'.
Hence, the correct answer is option A.

In the above sequence, the sum of the opposite positions of letters in the English alphabetical order is the same.
(IO : DT) →
The opposite of I = R(18)
The opposite of O = L(12)
R + L → 18 + 12 = 30
The opposite of D = W(23)
The opposite of T = G(7)
W + G = 23 + 7 = 30
On checking option B:
(MG : KI) →
The opposite of M = N(14)
The opposite of G = T(20)
N + T → 14 + 20 = 34
The opposite of K = P(16)
The opposite of I = R(18)
P + R = 16 + 18 = 34
Hence, Option B is correct.