Maths & Logical Reasoning Test - 1 - SSC CGL MCQ

Formula Used:

tan θ = perpendicular/base

Calculation:

We know that

⇒

⇒

⇒

In ΔBCA, we know that:

⇒

⇒

⇒

∴ The height of the tree AD = AC + BC

⇒

⇒ m

Calculation:

Store Q sold 198 mobile phones in 2013.

Store S sold 205 mobile phones in 2015.

Difference = (205 - 198 = 7).

∴ Option 2 is the correct answer.

Given:

√3 = 1.732

Concept used:

√(a x a x b) = a√b

Calculation:

⇒

⇒

⇒ 7√3 - √3 - 5√3

⇒ √3 = 1.732

∴ = 1.732

Given:

P(E) = 1/4, P(F) = 1/3 and P(E ∩ F) = 1/5 

Concept used:

By definition of P(E or F) under axiomatic approach(also called addition theorem) we know that: P(E∪F) = P(E) + P(F) – P(E∩F)

Calculation:

P(E) = 1/4

P(E̅) = 1 - (1/4)

⇒ 3/4

P(F) = 1/3

P(F̅) = 1 - (1/3)

⇒ 2/3

P(E ∩ F) = 1/5

P(E̅ ∩ F̅) = 1 - (1/5)

⇒ 4/5

Now,

P(E̅ ∪ F̅) = P(E̅) + P(F̅) - P(E̅ ∩ F̅)

⇒ 3/4 + 2/3 - 4/5

⇒

⇒ 37/60

Now,

P(F̅/E̅) = P(E̅ ∪ F̅)/P(E̅)

⇒ 37/60 ÷ 3/4

⇒ 37/45

∴ The required answer is 37/45.

Given:

Selling price of mixture = Rs.20

Formula:

%Profit = [(SP - CP)/CP] × 100

Calculations:

Cost price of mixture = (100/125) × 20

⇒ Rs.16

Price of water is Rs. 0

To gain 20% he have to manage the price by mixing water.

By the rule of alligation,

∴ Ratio of water to chemical = 9 : 16

Given:
Initial price of LPG cylinder = Rs. 776
New price of LPG cylinder = Rs. 970
Formula Used:
Percentage reduction in consumption = [(New Price - Old Price) / New Price] × 100
Calculation:
⇒ Percentage reduction = [(970 - 776) / 970] × 100
⇒ [194 / 970] × 100
⇒ 0.2 × 100
⇒ 20%
∴ the correct option is option 2.

Given:

Height of a tree = 27 m

From the top of this tree, the angles of depression of the top and the foot of the other tree are 30° and 60° respectively

So, The angles of elevation from the top and base of another tree to the top of this tree will be 30° and 60° respectively.

Formula used:

tan30° = 1/√3 and tan60° = √3

Calculation:

Let AB, and CD be the two trees and AC be the river.

Then, AB = 27 m

Let AC = x m and CD = h m. ∠ACB = 60°, and ∠EDB = 30°

⇒ AB/AC = tan60° = √3

⇒ AC = AB/√3 = 27/√3

⇒ AC = = 9√3 = 15.57 m

⇒ DE = AC = 9√3 m

⇒ BE/DE = tan30° = 1/√3

⇒ BE = 9√3 × (1/√3 ) = 9 m

∴ CD = AE = AB - BE = (27 - 9) = 18 m

Concept -

let the polynomial be p(x) then p(x) = 0 gives you the zeros of the polynomial.

Explanation -

We have the polynomial 9x2 - 4

Now for the zeros of the polynomial -

9x2 - 4 = 0

⇒ 9x2 = 4

⇒ x2 = 4/9

⇒

Hence option (1) is true.

Given:

Length of rectangle = 65m

Breadth of rectangle = 48m

Formula used:

Area of rectangle = Length × Breadth

%Change = [(Change in value)/(Initial value)] × 100

Calculation:

Initial area of rectangle = 65 × 48 = 3120 m²

Final length = 120/100 × 65 = 1.2 × 65 = 78 m

Final breadth = 90/100 × 48 = 0.9 × 48 = 43.2 m

⇒ Final area = 78 × 43.2 = 3396.6 m²

Here, the initial area is less than the final area i.e. area is increased.

Change in area = 3396.6 - 3120 = 249.6

% Change = 249.6/3120 × 100 = 0.08 × 100 = 8

Hence, the area of the rectangle is increased by 8%.

Formula Used:

Let the total income be I .

Total donations = 13% + 12% + 14% + 16% = 55%

Remaining income after donations = 45% of I

Given that this remaining income is equal to his savings:

Calculation:

⇒

⇒

Amount donated to the institution for visually impaired:

⇒

∴ The correct answer is option 5,785.

⇒ AB = x      .........(2)
Comparing 1 & 2  we get  (x + 20) / √3 = x

Hence, option (D) is correct.

As, the volume of solid remains same

x = 6 cm
So surface area = 4πr²
= 4 × π × 6 × 6 = 144π
Hence, option C is correct.

When a train crosses a platform, it covers its length and the platform’s length combined and the train crosses a pole, it covers only its length.
The trains are running at a constant speed, so, the covered distance (length) is proportional to time.
Length → Train A ꓽ Platform M = 20 ꓽ (64 – 20) = 5 ꓽ 11
Let, the length of train A be 5a and the length of platform M be 11a
Length → Train B ꓽ Platform N = 24 ꓽ (72 – 24) = 1 ꓽ 2
Let, the length of train B be a and the length of platform N be 2b


Let,
Length of train A = 16 × 5 = 80
Length of train B = 55 × 1 = 55
Train A can travel the distance equal to its length in 20 seconds
Train B can travel the distance equal to its length in 24 seconds

Hence, Option D is correct.

Let, Abhik’s weight be 100
Souvik’s weight = 80% of 100 = 80
Mayukh’s weight = 80 × 3 = 240
Rupam’s weight = 150% of 240 = 360
Avijit’s weight = 40% of 360 = 144
So, Souvik’s weight is the least.
Hence, Option B is correct.

Percentage of students who passed in at least one subject = 30% + 25% – 15% = 40%
Failed in both the subjects = 100 – 40% = 60%
Therefore, the total number of students

Hence, Option C is correct.

x⁶ + 1 = 0
= x¹² (x⁶ + 1) + (x⁶ + 1) + 6
= x¹² × 0 + 0 + 6
= 6
Hence, Option A is correct.

Preparing the family tree using the following symbols:

Given :

1. A @ B means A is the sister of B,

2. A # B means A is the mother of B,

3. A * B means A is the father of B

On decoding ‘P * Q @ R # S’ means P is the father of Q, Q is the sister of R, R is the mother of S.

Drawing the family tree as per the given information:

Therefore, above diagram clearly shows the P is Grandfather of S

Hence, "P is the grandfather of S" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

In figure D, the arrow which is along the circumference of a circle is in the opposite (anticlockwise) direction to the arrows in the other figures.

In figures A, B, and C, this arrow is moving in the clockwise direction.

Hence, figure D does not belong to the group.

The correct order of the given words according to the English dictionary is:
6. Farther

2. Fascinating

3. Fashionable

1. Fasting

7. Father

5. Fault

4. Faux

So, the correct order is 6, 2, 3, 1, 7, 5, 4.

Hence, the correct answer is option (2).

From the statements given:

I. The police has increased vigilance during late night hours.
II. Incidents of petty crimes have reduced in the late night hours.

Statement I is an action which was taken in order to reach to an effect and statement II is the effect that was caused by the action taken such that when police increased vigilance during late night hours the effect of that was incidents of petty crimes have reduced in the late night hours.
So statement I is the likely cause and statement II is its likely effect.

Hence the correct answer is option 4.

From the above diagrams we can say that,

Drawing the diagrams,

(1) Q – Z ÷ U × K

This is not correct, because the last condition U × K is not satisfied.

(2) Q – Z × U ÷ K

This satisfies the condition.

(3) K – Z ÷ U × Q

This is not correct, because the condition U × Q is not satisfied.

(4) K – U ÷ Z × Q

This is not correct because, the condition Z × Q is not satisfied.

‘Q – Z × U ÷ K’ represents that ‘U is the daughter of Q’.

Hence, option 2 is the correct answer.

The logic followed here is :-

The given word is coded as "X-Y".

X = Number of letters in a word.

Y = Sum of opposite alphabet positional letters of a word.

'GAME' is written as '4-82'.

Number of letters in word 'GAME' = 4

Sum of opposite alphabet positional letters = 20 + 26 + 14 + 22

Sum of opposite alphabet positional letters = 82

And

'MUSIC' is written as '5 -70'

Number of letters in word 'MUSIC' = 5

Sum of opposite alphabet positional letters = 14 + 6 + 8 + 18 + 24

Sum of opposite alphabet positional letters = 70

Similarly,

'SPRING' will be written as :

Number of letters in word 'SPRING' = 6

Sum of opposite alphabet positional letters = 8 + 11 + 9 + 18 + 13 + 20

Sum of opposite alphabet positional letters = 79

∴ Here, 'SPRING' is written as '6-79'.

Hence, the correct answer is "6-79".

Rule: In the open dice opposite surface always exist in a straight line at the gap of 1 box.

Opposite pairs;

G = K

J = F

B = A

Only option 2 can be made.

Hence, the answer is Option 2.

Distance between L and G: IH – JK = 20 – 8 = 12m.

Thus we get “12m”.
Hence, option A is correct.

Common explanation:
Reference:
Point G is 25m to west of point F.
Point H is 5m to west of point G.
Point I is 20m to north of point H.
Point J is 12m to east of point I.
Point K is 8m to south of point J.
Point L is 7m to west of point K.
Inference:
From above statements, we get following figure:

The pattern of the given group of letters are: 

We can clearly observe from the above figure, except RPOQ all others group of letters have the same pattern.
Hence, option C is correct.

(32 : 256) → [(32 + 16)/3]² = 16² = 256
(44, 400) → [(44 + 16)/3]² = 20² = 400
Now, on checking option B,
(53, 529) → [(53 + 16)/3]² = 23² = 529
Hence, Option B is correct.

Hence, Option D is correct.

Using the above information we get,

R is the grand-daughter of A.
Hence option B is correct.