Maths & Logical Reasoning Test - 5 - SSC CGL MCQ

sin(3x - 20°) = cos(3y + 20°)

⇒ sin(3x - 20°) = sin [90° - (3y + 20°)]

⇒ 3x - 20° = 90° - 3y - 20°

⇒ 3x + 3y = 90°

⇒ x + y = 90°/3

⇒ x + y = 30°

Now, we know that

⇒ tan (x + y)

⇒ tan 30°

Given:

Train 1 takes 7 seconds to pass a man.

Formula Used:

Speed = Distance / Time

Calculation:

Let the length of Train 1 be (L) meters. Thus, the length of Train 2 is (2L) meters.

For Train 1:

⇒ Speed of Train 1 = (L / 7) meters/second

For Train 2:

⇒ Speed of Train 2 = (2L / 10) meters/second = (L / 5) meters/second

When they pass each other, the total distance covered will be their combined lengths = (L + 2L = 3L) meters.

⇒ Relative Speed = ((L / 7) + (L / 5))

⇒ (5L + 7L) / (35)

⇒ (12L / 35) meters/second

The time for them to pass each other:

⇒ Time = Distance / Speed

⇒ Time = (3L) / ((12L / 35))

⇒ (3L × 35) / (12L)

⇒ (105 / 12) seconds

⇒ ≈ 8.75 seconds

Rounded to the nearest integer, the time taken by the trains to pass each other will be 9 seconds.

Formula used:

Area of equilateral triangle = (√3/4) (side)²

Area of Hexagon = (3√3/2)a²

Calculation:

AB = 54 cm.

As all similar triangles are also equilateral. So,

ΔANM, ΔOCP, ΔQPX are equilateral triangles.

MN = MR = NO = OP = PQ = QR = 54/3 = 18 cm

MNOPQR is a regular hexagon.

Required area = 3√3 × (18)²/2 = 486√3 cm²

Given:

Ratio of three different types of old coins = 3 : 5 : 7

Value of old coins = 1 rupee, 5 rupees, and 10 rupees respectively.

Total value of box coins = Rs. 2,842

Formula Used:

Total value = (Number of 1 rupee coins × 1) + (Number of 5 rupees coins × 5) + (Number of 10 rupees coins × 10)

Calculation:

Let the number of 1 rupee, 5 rupees, and 10 rupees coins be 3x, 5x, and 7x respectively.

Total value = (3x × 1) + (5x × 5) + (7x × 10)

⇒ 2842 = 3x + 25x + 70x

⇒ 2842 = 98x

⇒ x = 2842 / 98

⇒ x = 29

Number of 10 rupees coins = 7x = 7 × 29 = 203

The number of 10 rupees coins is 203.

Given:

10 chairs and 5 tables were purchased for Rs. 17,500.

Calculation:

Let the average cost of a table be x.

10 chairs cost = 10 x 1000 = Rs. 10,000

5 tables cost = 5x

Total cost = 10,000 + 5x = 17,500

Subtracting 10,000 from both sides, we get:

5x = 7,500

x = 1,500

Therefore, the average cost of a table is Rs. 1,500.

Given:

The image of the point (3, 4) in x - axis.

Concept used:

The reflection of point (x, y) along x axis is (x, -y)

The reflection of this point along y axis is (-x, y)

Calculations:

To find the reflection of the point along the x-axis, the abscissa remains constant.

So, the reflection of point (3, 4) along the x-axis is (3, -4).

∴ The answer is (3, -4)

Concept used:

1 day = 24 hours, 1 hours = 60 min, 1 min = 60 sec

Calculation:

The number of minutes in 20 days = 20 × 24 × 60

Now, according to the question we have to consider the value as second and convert it to hours

So, 3600 sec = 1 hr

then, 20 × 24 × 60 sec = (20 × 24 × 60)/3600 = 8 hr

∴ The correct answer is 8 hr

There are two series
S1 : 1 + 4 + 7 + 10 + ……….. 25 terms
S2 : 3 + 5 + 7 + 9 + ………… 25 terms
S1:
Sum of n terms of a series with first term a, common difference d

a = 1, d = 3 and n = 25

S2:
a = 3, d = 2 and n = 25


Hence, option C is correct.

Let, 3 years ago, P’s age was 7a and Q’s age was 8a

84a + 144 = 88a + 132
4a = 12
a = 3
Q’s age was 3 years ago = 8 × 3 = 24 years
Q’s age 5 years ago = 24 – 2 = 22 years
Hence, Option A is correct.

A gives 5 chocolates
New number of chocolates B will have

New number of chocolates C will have

Reqd. Ratio = 14 : 5
Hence, Option B is correct.

6, 8, and 10 are Pythagoras triplet.
Thus, ΔPQR is a right-angled triangle



Distance = √(R² – 2 × r × R) = √5 cm
Hence, Option B is correct.

Let the usual speed = s km/hr

s = 80 km/hr

Hence, Option D is correct.

sin (A + B) = sin 150°
A + B = 150° ---- (1)
cos (A – B) = cos 30°
A – B = 30° ---- (2)
From (1) and (2), we get
A = 90° and B = 60°


Hence, Option C is correct.

Given:

Shilpa's position from left = 8th

Reena's position from Right = 17th

After interchanging:

Shilpa from the left = 14th

Total girls = [{(Position of Shilpa from the left) + (Position of Reena from the Right)} - 1]

⇒ Total girls = [(17 +14) - 1]

⇒ Total girls = 30

Hence, the correct answer is "30".

The pattern followed here is:

Option 1: 87 : 75 → 8 + 7 = 15 × 5 = 75

Option 2: 79 : 64 → 7 + 9 = 16 × 4 = 64

Option 3: 73 : 40 → 7 + 3 = 10 × 4 = 40

Option 4: 67 : 52 → 6 + 7 = 13 × 4 = 52

Hence, ‘87 : 75’ is the odd pair.

Given:

Four members - Ravi, Rajiv, Rahul and Rohit likes Mercedes, BMW, Thar and Audi. Sitting around a circular table facing the center.

Explanation:

Statement I: Rohit likes Mercedes and sits opposite to the one who likes Audi. And who likes Thar and BMW are immediate neighbour of Rahul and sits opposite to each other.

So, according to the final arrangement of Statement I, we found that Rahul likes Audi.

Statement I alone, is sufficient to answer the question.

Statement II: Rajiv likes BMW and sits Opposite to the one who likes Thar. Rohit sits opposite to the one who likes Audi.

So, according to the final arrangement of Statement II, Audi may be liked by Rahul or Ravi.

Statement II alone, is not sufficient to answer the question.

Data in statement I alone is sufficient to answer the question while data in statement II is not.

Hence, the correct answer is 'Option 4'.

The statement says that human body can produce Vitamin D on its own with the help of sun exposure.

Therefore, it can be safely assumed that human body does not have to depend on food for its required intake of Vitamin D.

Thus, assumption I is implicit.

However, the statement does not discuss the deficiency of Vitamin D of anyone.

Therefore, assumption II is not implicit.

The mirror image for given is as follows :

Thus, the correct answer is "Option 1".

Thus, the correct answer is option 4.

Statement I : 'He Li Be B C' means 'He is a good singer' and 'Be N O F Ne' means 'She will sing good songs'.

We can see that "GOOD" is coded as "Be".

Statement II: 'He Li Be B C' means 'He is a good singer' and 'Be N C F Ne' means 'He will sing good songs'.

We can not decide the code for "GOOD" from this statement.

Hence, Statement I alone is sufficient while II alone is not sufficient

As per the given information the sitting arrangement:

1. Suman sits second to the right of Gagan.

2. Gagan is an immediate neighbour of Pran and Vyom.

Case 1:

Case 2:

3. Kiran sits second to the right of Vyom and Samir is an immediate neighbour of Kiran.

Here, Pran is sitting third to the right of Suman.

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

Hence, option D is correct.

Checking equation: 4,
On applying given operations we get,
34 × 6 – 16 + 221 ÷ 13 = 205
34 × 6 – 16 + 17 = 205
204 – 16 + 17 = 205
221 – 16 = 205
205 = 205
Hence, Option D is correct.

Logic: Except option D, in rest all the sum of these numbers gives a perfect square number.
(515, 854) → 515 + 854 = 1369 = 37²
(439, 786) → 439 + 786 = 1225 = 35²
(355, 606) → 355 + 606 = 961 = 31²
(456, 615) → 456 + 615 = 1071
Hence, Option D is correct.

Checking C1: Some Low are not Triangle
Since some Low are High and no High is Triangle, which means some Low which are High cannot be Triangle. Therefore, conclusion I follows.
Checking C2: Some Circle are not High
Only a few Line are Triangle and all Line are Circle, which means Some Circle are Triangle and no Triangle is High, which means some Circle which are Triangle cannot be High. Therefore, conclusion II follows.
Hence, Option B is correct.

Checking C1: Some Tough are Key
We can see that in the Venn diagram only water is tough. Thus, C1 doesn’t follow.
Checking C2: No Key is Tough
We can see that in the Venn diagram only water is tough so no key is tough is true. Thus, C2 follows.
Checking C3: Some Pages are Key
We can see that in the Venn diagram there is no direct relation between Pages and Key. Thus, C3 doesn’t follow.
Hence, Option D is correct.

The numbers in the matrix follow the below-mentioned logic:
Column 1: (24, 624, 16) → 24² + (16 × 3) = 624
Column 2: (19, 432, 24) → 19² + (24 × 3) = 433
Similarly, Column 3: (26, ?, 22) → 26² + (22 × 3) = 742
Hence, Option B is correct.

The expression in the question can be rewritten as follows, J < G < Z < W < K ≤ A < S < N, O ≤ K.
From this expression, we can conclude that only 1-B and 1-C applies.
Hence, Option B is correct.

The numbers in the matrix follow the below-mentioned logic:
Row 1: (84, 15, 180) → (8 + 4) × 15 = 180
Row2: (96, 17, 255) → (9 + 6) × 17 = 255
Similarly Row3: (?, 24, 336) →
Now checking option C:
(6 + 8) × 24 = 14 × 24 = 336
Hence, Option C is correct.

All labourers are not dedicated.

All professionals are not dedicated.

Labourer can't be a professionals.

So, we can clearly say that option B is correct.

Labourer: A person doing unskilled manual work for wages.

Professional: A person competent or skilled in a particular activity.