Maths & Logical Reasoning Test - 3 - SSC CGL MCQ

Given:

Speed for the first quarter of the journey: 40 km/h
Speed for the second quarter of the journey: 50 km/h
Speed for the third quarter of the journey: 60 km/h
Speed for the last quarter of the journey: 70 km/h

Concept or Formula:

The average speed for the whole journey can be calculated as total distance divided by total time taken.

The average speed will be given by 4/(1/speed1 + 1/speed2 + 1/speed3 + 1/speed4)

Calculation:

Since each quarter of the journey is equal in length, let's assume the distance of each quarter to be 'd' . Thus, total distance = 4d.

Time taken = distance/speed.

⇒ Time taken for first quarter = d/40

⇒ Time taken for second quarter = d/50

⇒ Time taken for third quarter = d/60

⇒ Time taken for fourth quarter = d/70

Add up the individual time taken to find the total time taken for the journey.

⇒ Total time taken = d/40 + d/50 + d/60 + d/70

Average speed = Total Distance / Total Time Taken

⇒ 4 / (1/40 + 1/50 + 1/60 + 1/70)

⇒ 52.66 km/h

∴ The average speed of the car for the whole journey is approximately 52.66 km/h.

Given:

The total distance = 150 km

Formula used:

S = D/T Where S = The speed, D = The distance, and T = The time

Calculation:

Let us assume the speed of the car be S and time taken by car to cover 150 km be T

⇒ ST = 150 ----(1)

⇒ If speed is decrease by 5 km/h

⇒ (S - 5) × (T + 1) = 150

⇒ ST - 5T + S - 5 = 150 ----(2)

⇒ By equation (1) and (2)

⇒ S² - 5S - 750 = 0

⇒ By solving

⇒ S = 30, -25

⇒ The speed of the car = 30 km/h

∴ The required result will be 30 km/h.

Calculation:

The total number of boys studying in school P and Q = 280 + 365 = 645

The total number of girls in the P and Q schools together = 350 + 260 = 610

Difference = 645 - 610 = 35

∴ Option 4 is the correct answer.

Given:

The angle of elevation of the top of a tower of height x meter from a point on the ground is found to be 60°

By going y metre away from that point, it becomes 30°

Concept used:

tanθ = P/B

Here P = perpendicular, B = base

Calculation:

According to the question,

tan60° = AB/BC

⇒ √3 = x/BC

⇒ BC = x/√3 -------(1)

Again, tan30° = AB/BD

⇒ 1/√3 = AB/BD

⇒ 1/√3 = x/BD

⇒ BD = √3x

BD = BC + CD

⇒ √3x = x/√3 + y [From equation (1)]

⇒ √3x = (x + √3y)/√3

⇒ 3x = x + √3y

⇒ 2x = √3y

∴ Required answer is Option 3

Given:

Distance = 30 km

Amit's time is 2 hours more than Sameer's time.

Amit's time with double speed is 1 hour less than Sameer's time.

Concept used:

Distance = Speed × Time

Calculation:

Let, Sameeer's speed = s km/hr

Sameer's required time = 30/s hr

According to the question,

Amit's required time = 30/s + 2 = (30 + 2s)s hr

So, Amit's speed = 30 ÷ (30 + 2s)/s = 30s/(30 + 2s) km/hr

30 ÷ (2 × 30s/(30 + 2s)) = 30/s - 1

⇒ 30 ÷ 60s/(30 + 2s) = (30 - s)/s

⇒ (30 + 2s)/2s = (30 - s)/s

⇒ s × (30 + 2s) = 2s × (30 - s)

⇒ 30s + 2s² = 60s - 2s2

⇒ 4s² = 30s

⇒ s = 7.5 km/hr

So, Amit's speed = (30 × 7.5)/(30 + 2 × 7.5) = 5 km/hr

∴ Amit's original speed is 5 km/hr.

We know equation of line: y = mx + c

y = −x + 1

y = − x + 2

Both the slopes are same = -1

We know that 2 lines never intersect each other if they have same slope

∴ No intersection point exists.

HCF of (209 - 5) and (347 - 7)

HCF of (204 and 340)

204 = 2 × 2 × 3 × 17

340 = 2 × 2 × 5 × 17

HCF will be 2 × 2 × 17 = 68, according the option, 17 is the correct answer.

∴ 17 is the greatest number when divide 209 and 347 leaves remainder 5 and 7 respectively.

Given :

44% of the students are girls.

The number of boys is 448.

Let the total number of students be x.

Number of boys = 448 Number of girls = x - 448 (since the rest are girls)

We know that the percentage of girls is 44%.

44% of x = x - 448 0.44x = x - 448 0.56x = 448 x = 448 / 0.56 x = 800

Number of girls = 44% of the total number of students Number of girls = 0.44 × 800 Number of girls = 352

Hence, the number of girls in the school is 352.

Given:

(7 × 4) + (2 × 12) - ­((24/8) + (121/11) × 2)

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(7 × 4) + (2 × 12) - ­((24/8) + (121/11) × 2)

⇒ (28) + (24) - ­((3) + (11) × 2)

⇒ 28 + 24 - ­(3 + 22)

⇒ 28 + 24 - ­25

⇒ 52 - ­25

⇒ 27

∴ (7 × 4) + (2 × 12) - ­((24/8) + (121/11) × 2) = 27

Given:

Total distance of journey = 192 km.

Time = 2 hours

Formula Used:

Speed = distance/time

Calculation:

Let the speed of the fast train = x km/h

According to question

Speed of the slow train = Speed of fast train - 16 = (x -16) km/h

Again,

Time of fast train = time of slow train - 2

⇒

⇒

⇒

⇒ x(x -16) = 96 × 16

⇒ x² - 16 x -1536 = 0

⇒ x² - 48 x + 32 x - 1536 =0

⇒ (x - 48)(x + 32) = 0

x = 48, -32

The speed of a fast train x = 48 km/h

The speed of the slow train = (x -16) = 48 -16 = 32 km/h

∴ The correct answer is 48 km/h and 32 km/h.

Following common explanation we get
Asus has the maximum average selling price during 2011-2015
Hence, option (C) is correct.
Common explanation :

Amount spent on others and education together = (7 + 20)% of 4.8 lakhs = 27% of 4.8 lakhs = 1.296 lakhs 
Hence, option C is correct.

Investment ratio → A ꓽ B = 43675 ꓽ 61145 = 5 ꓽ 7
Profit ratio → A ꓽ B = 5 ꓽ 7 (Time constant)
Let,
The profit earned by A = 5 units
The profit earned by B = 7 units
They divided 1/3 of the total profit equally, so the difference between the profit share of A and B is in

Difference → 7 – 5 = 2 units = 8472
2/3 of the total profit earned by them


Hence, Option A is correct.

Hence, option A is correct.

In ΔQOS and ΔPOT
By figure, we get that
∠OQS = ∠OPT ---- (1)
In ΔQOS and ΔPSR
∠OSQ = ∠PSR (90°)
∠OQS = ∠SPR (From eq (1))
ΔQOS ~ ΔPRS

QS = PS (as QO = PR is given) ---- (2)
In ΔPQS
∠PQS = ∠SPQ (from eq. 2)

In ΔPQR
∠QPR = 180° – 45° – 60° = 75°
Hence, Option A is correct.

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols move as shown below and the rectangle changes into X.

From Figure (2) to (3):

The symbols move as shown below and the symbol X changes into 9.

From Figure (3) to (4):

The symbols move as shown below and the symbol U changes into =.

From Figure (4) to Answer Figure (5):

The symbols move as shown below and the symbol D changes into L.

Hence, the correct answer is "Option (4)".

The pattern follows here is;

Similarly;

Hence, "ERUTMPCO" is the correct answer.

The logic followed here is :-

Fear of height is called Acrophobia.

Similarly,

Fear of vomiting is called Emetophobia.

Hence the correct answer is "Emetophobia".

Additional Information:

Argument I claims that advertisements are immoral without any explanation as to why this is the case. It does not point out its negative impact on television viewers either.

Thus, this demerit lacks the explanation needed for it to be considered a strong reason to ban advertisements on television.

Therefore, argument I is not strong.

Argument II points out the benefit of ‘increase in revenue’ and explains the positive impact of this increased revenue for viewers.

The given figure when unfolded is as follows:

Hence, the correct answer is "Option (4)".

The logic follow here:

If we consider the center rectangle black area as a front then the semi-circle is on the right side and the arrow is on the left side.

Check all the options:

Figure (A):  → Semi-circle is on the right side and the arrow is on the left side.

Figure (B):  → Semi-circle is on the left side and the arrow is on the right side.

Figure (C): → Semi-circle is on the right side and the arrow is on the left side.

Figure (D): → Semi-circle is on the right side and the arrow is on the left side.

Figure (E): → Semi-circle is on the right side and the arrow is on the left side.

Hence, "Option 2" is the correct answer.

The Logic here is as follows:

(1^st Number - 1) × (2^nd number - 1) = 3^rd Number

In (12, 14, 143)

(1st Number - 1) × (2nd number - 1)

= (12 - 1) × (14 - 1)

= (11 × 13)

= 143 = 3^rd Number

Now check the all options,

Option (1): (16, 10, 235)

(1st Number - 1) × (2nd number - 1)

= (16 - 1) × (10 - 1)

= (15 × 9)

= 135 ≠ 3rd Number

Option (2): (15, 19, 252)

(1^st Number - 1) × (2^nd number - 1)

= (15 - 1) × (19 - 1)

= (14 × 18)

= 252 = 3^rd Number

Option (3): (12, 18, 246)

(1st Number - 1) × (2nd number - 1)

= (12 - 1) × (18 - 1)

= (11 × 17)

= 187 ≠ 3rd Number

Option (4): (17, 12, 134)

(1st Number - 1) × (2nd number - 1)

= (17 - 1) × (12 - 1)

= (16 × 11)

= 176 ≠ 3rd Number

Hence, the correct answer is "(15, 19, 252)".

73 × 69 × 43 = 185 and 41 × 53 × 68 = 162 can be written as

73 + 69 + 43 = 185 [Here code of × is + ]

41 + 53 + 68 = 162

Similarly, 11 × 31 × 71 can be written as

11 + 31 + 71 = 113.

Therefore, 113 is the correct answer.

The logic follows here is :

2. Dreamer

4. Dreamland

1. Dreamlike

5. Dreamtime

3. Dreamy

Thus, the correct sequential order is "2 - 4 - 1 - 5 - 3".

LOGIC: (First Number - Second Number) × 2 = Third Number

In (33, 6, 54) →

(33 - 6) × 2 = 27 × 2 = 54

And;

In (22, 7, 30) →

(22 - 7) × 2 = 15 × 2 = 30

Similarly;

In (26, 8, 36) →

(26 - 8) × 2 = 18 × 2 = 36

Hence, the correct answer is "(26, 8, 36)".

Given Statements:

I. All Z are Y.

II. Some Y are B.

The least possible Venn diagram for the given statement is:

Conclusions:

Conclusion I: False ("Some B are not Z" is not true because there is no negative relation between B and Z. It may be possible but not definitely true. In syllogism, we take the definite cases as true. So this conclusion not follow.)

Conclusion II: False ("Some Y are not Z" is not true because there is no negative relation between Y and Z. It may be possible but not definitely true. So, this conclusion also not follow.)

Conclusion III: True ("Some Z are Y" is true because when all Z are Y is given then "some Z are Y" is also true. Please note that "some" is a subset of "all". For example, when all boys are male, then "some boys are male" is also true.)

So, Only conclusion III follows.

Hence, the correct answer is "Option 3".

Mistake Points

Negative Conclusions will never be definitely true when a given statement is positive.
Here, Conclusion I & II is negative, so it will be true in possibility only.

Using the above information, we get the following arrangement:

We get “P” visited Delhi on Wednesday.
Hence, Option B is correct.

Using the above information we get,

P sits second to the left of J.
Hence, option B is correct.

Checking equation: 2,
On applying given operations we get,
18 × 25 + 135 – 375 ÷ 15 = 560
18 × 25 + 135 – 25 = 560
450 + 135 – 25 = 560
585 – 25 = 560
560 = 560
Hence, Option B is correct.

Checking C1: W < T
W = V < S < T, so the given conclusion W < T is true.
Checking C2: I < T
T > S ≥ P > I, so the given conclusion I < T is true.
Checking C3: T > O
T > S ≥ P > O, so the given conclusion T > O is true.
Checking C4: U > V
U > H ≥ I < P ≤ S > V, so the given conclusion U > V is false.
Hence, Option D is correct.