Maths & Logical Reasoning Test - 2 - SSC CGL MCQ

Given:

A sector of angle = 60°

Area of sector = 18(6/7) cm² = 132/7

Formula used:

Area = πr²θ/360°

Calculation:

132/7 =

⇒ 6 × 6 = r²

⇒ r = 6

∴ The correct answer is 6 cm.

Given:

Sale price of a house = Rs. 52 lakhs

Total commission = Rs. 2.34

Formula:

x as a percentage of y = x/y × 100

Calculation:

Commission received from purchaser = 2.34/2 lakh = Rs. 1.17 lakh

∴ Percentage of commission = (1.17/52) × 100 = 2.25%

Given:

In ΔLMN, OP is a line segment drawn parallel to the side MN

OP intersects the sides LM and LN at O and P

LM = 15 cm, OM = 4 cm, and PN = 5 cm

Formula:

If ΔABC ∼ ΔPQR, then

AB/PQ= BC/QR = AC/PR

Calculation:

LM/OM = = LN/PN

⇒ 15/4 = LN/5

⇒ LN = (15 × 5)/4

⇒ LN = 75/4 = 18.75 cm

∴ Option 2 is the correct answer.

Given:

The average age of 8 coworkers = 16 years

2 new colleagues join the average age, increases by 1 year.

Formula Used:

Average = Sum of total observations / Total no. of observations

Calculation:

The sum of average age of 8 coworkers = 8 × 16 = 128 years

According to the question,

After adding the age of new 10 coworkers,

The average age is 17 years

The sum of ages after adding new coworkers

⇒10 × 17 = 170 years

The age of new coworkers = 170 - 128 = 42 years

The average age of new colleagues = 42/2 = 21 years.

∴ The correct answer is 21 years.

Given:

Original price of stock for 100 shares = Rs. 1,000

Increase in first year = 30%

Decrease in second year = 20%

Formula used:

Price after increase = Original price × (1 + Increase %)

Price after decrease = Price after increase × (1 - Decrease %)

Calculation:

Price after first year

⇒ 1000 × (1 + 0.30) = 1000 × 1.30 = Rs. 1300

Price after second year

⇒ 1300 × (1 - 0.20) = 1300 × 0.80 = Rs. 1040

Final value of the investment after 2 years = Rs. 1,040

Given:

There were 46 students in a boys hostel.

Due to the admission of eight new students the expenses of the hostel mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1.

Calculation:

Let 'x' be the original expenditure of the hostel mess in rupees per day.

Case 1:

The total number of students = 46

The average expenditure per head = Rs. (x/46) per day

Case 2: When 8 new students are admitted

The total number student = 46 + 8 = 54

The new average expenditure per head = Rs. per day

According to the problem,

The average expenditure per head diminished by Rs 1,

Therefore,

⇒ = 1

⇒ = 1

⇒ 8x = (46 × 54) + (46 × 42)

⇒ 8x = 46 × (54 + 42)

⇒ x = 46 × 12

⇒ x = Rs. 552

The original expenditure of the mess = Rs. 552

Therefore, "Rs. 552" is the required answer.

Given:

Concept used:

Using the BODMAS rule:

Calculation:

According to the question,

⇒

⇒

⇒ ?² = × 16 × 11

⇒ ?² = × 16 × 11

⇒ ?2 =

⇒ ?2 =

Therefore, "" is the required answer.

Given:

Quantity of pure alcohol initially in the jar = 120 l

The ratio of alcohol and water = 8 : 3

Quantity of solution removed = 55 l

Quantity of water added = 18 l

Calculation:

Quantity of the water in the initial solution = (3/8) × 120 = 45 l

Quantity of alcohol in the final solution = 120 – (8/11) × 55

⇒ 120 – 40 = 80 l

Quantity of water in the final solution = [45 – {(3/11) × 55} + 18]

⇒ 45 – 15 + 18 = 48 l

⇒ The required percentage = {(48/120) × 100} = 40%

∴ The required percentage is 40%.

Given:

First term = x3y

Second term = xy3

Formula Used:

mean proportion = √(first term × second term)

Calculation:

⇒ √((x³y) × (xy³)) = √(x⁴y⁴) = x2y2

∴ Option 1 is the correct answer.

When two dices are rolling, we get,

{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

The sample space = 36

Only three samples are there that have a sum of 10 i.e. (4,6), (5,5), and (6,4)

The probability of getting the sum of 10 = 3/36 = 1/12

∴ The probability of getting the sum of 10 is 1/12.

Given:

Cost of first variety of pulses = Rs. 18 per kg.

Cost of second variety of pulses = Rs. 22 per kg.

Cost of the mixture = Rs. 19.50 per kg.

Formula Used:

Let the ratio in which the two varieties are mixed be x : y. Then, the rule of allegation gives us:

Price of second variety - Mean Price / Mean Price - Price of first variety = Quantity of first variety / Quantity of second variety

Calculation:

⇒ (22 - 19.50) / (19.50 - 18)= x / y

⇒ 2.50 / 1.50 = x / y

⇒ 25 / 15 = x / y

⇒ x / y = 5 / 3

∴ The ratio in which the two varieties must be mixed is 5:3.

Let the parts be X and Y
SI on X for 9/2 years at 28/3% p.a. = 2 × ( SI on Y for 13/4  years at 12% p.a)


Difference between X and Y

Hence, option C is correct.

∠BAC = 40°
Hence, option D is correct.

∠AOB = 360° – 90° – 90° – 50° = 130°

(angle on centre is twice than on circumference)
∠CBQ = ∠ACB = 65° (AC || PB)
∠CAB = ∠CBQ = 65° (alternate segment)
In ΔACB
∠ABC = 180° – 65° – 65° = 50°
Hence, Option B is correct.

Reqd. Ratio = 3 : 2
Hence, Option A is correct.

According to the given information:

• Deveshi got 23^rd rank from the top and Tanvi got 18^th Rank from the bottom.
• Only four students have ranked in between the ranks of Deveshi and Tanvi.
• Deveshi got a higher rank than Tanvi.

The number of students in a row = deveshi position from top + 4 students + tanvi position from bottom.

= 23 + 4 + 18

= 45

Hence, the correct answer is "45".

According to the sequence in the dictionary:

The correct order of the given words is:

4 Magnet

2 Marvellous

1 Memorable

3 Milestone

5 Mischievous

Hence, the correct answer is "4, 2, 1, 3, 5".

The code language have a pattern :
GENIUS : IUNGES

And

HOLDER : DELHOR

Similarly,

Hence, the correct answer is HTGLIS.

Clearly, 1, 26, 31 represent the group of bottles which are not brown.

The given statement is: M = N ≥ Q > R = W ≤ Z

Conclusions:

I. M > R → True (as M = N ≥ Q > R given; so M > R is true).

II. Z ≥ R → True (as R = W ≤ Z given; so Z ≥ R is true).

The pattern followed is:

For PLENTY,

For MORE,

Similarly, for MANY,

So, MANY is written as COAP.

Hence, the correct answer is "COAP".

The Pattern followed here is;

Hence, the correct answer is "72".

Preparing the family tree diagram by using the following symbols:

According to the statement:

1. In a family of eight people.

2. Scientist is married to a Teacher and has three sons, one Engineer, one Doctor, and one Actor.

3. The Actor's wife is a Dancer and aunt of Sarita and Sarita is the daughter of an Engineer.

4. Sarita, the daughter of an Engineer learns Science with her brother Mahesh. The final arrangement is,

Here, Doctor is the 'paternal uncle' of Mahesh.

Hence, the correct answer is "Paternal Uncle".

Grievous hurt would solicit sudden treatment and therefore without wasting time the child should be taken to hospital for treatment while also his family be informed simultaneously.
Hence, option A is the correct answer.

Hence, option C is correct.

The given word is coded as the sum of the opposite positional value of each letter.
MANAGE → NZMZTV → 14 + 26 + 13 + 26 + 20 + 22 = 121
DESIRE → WVHRIV → 23 + 22 + 8 + 18 + 9 + 22 = 102
Similarly, ADVISED → ZWERHVW → 26 + 23 + 5 + 18 + 8 + 22 + 23 = 125
Hence, Option B is correct.

We can see that in the word “Equivalent”, only 5 pairs of letters are there.
Forward Direction: IL, IN and LN
Backward Direction: EI and LQ
Hence, Option B is correct.

Using the above information, we get the following diagram:

We get Amit is in the North-east direction with respect to his initial position.
Hence, Option B is correct.

“Voltage are very heavy” → “ts mk sm bd”……………………..(1)
“Heavy weight are difficult” → “jm qk ts mk”………………….(2)
“Weight are heavy” → “mk ts jm” …………………………………..(3)
From 1, 2 and 3 we get the code for are/heavy → ts/mk
From 2 and 3 we get the code for weight → jm
Therefore, the code for difficult → qk
Hence, Option C is correct.

Checking C1: Some Sunday is Tuesday
We can see that in the Venn diagram no direct relation between Sunday and Tuesday, so conclusion 1 doesn’t follows.
Checking C2:  Some Monday being Wednesday is a possibility
We can see that in the Venn diagram some Monday being Wednesday is not a true relation because only Tuesday is Monday, so conclusion 2 doesn’t follows.
Hence, Option A is correct.