Maths & Logical Reasoning Test - 6 - SSC CGL MCQ

Given:

P and Q started a business with investment of Rs. 2400 and Rs. 3600 respectively.

If at the end of 3 years Q withdraws Rs. 1800,

Concept:

Ratio of profit shared = Ratio of the product of amount invested and time of investment

Calculation:

According to the question,

P started a business invested amount = Rs. 2400

Time of investment for P = 5 years

Q started a business invested amount = Rs. 3600

Time of investment by Q of Rs. 3600 = 3 years

Remaining amount of Q = Rs. 1800

Time of investment by P of Rs. 1800 = 2 years

Now, the ratio of investment for P and Q are:

⇒ P : Q = (2400 × 5) : (3600 × 3) + (1800 × 2)

⇒ P : Q = 120 : 108 + 36

⇒ P : Q = 120 : 144

⇒ P : Q = 5 : 6

Therefore, "5 : 6" is the required answer.

Concept used:

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space)

Calculation:

Total number of possibilities = 6³

Now,

Favorable outcomes = (1, 1, 3), (1, 2, 2), (1, 3, 1), (2, 1, 2), (2, 2, 1), (3, 1, 1)

Total favorable outcomes = 6

So, required probability = 6/216

⇒ 1/36

∴ The required answer is 1/36.

Concept:

The difference of any two sides is always less than that of the 3rd side.

Calculation:

To get an idea about the length of OB there is no need to consider point A.

OC = √50 = 7.07

BC = 2

In a triangle, the difference of any two sides is always less than that of the 3^rd side.

So in ΔOBC:

OB > 7.07 − 2 > 5.07

OB² > 25

∴ Option (a) is correct.

Formula used:

1. tan θ = sin θ/cos θ
2. cot θ = cos θ/sin θ
3. (a - b)² = a² - 2ab + b²

Calculation:

Statement 1:

Taking L.H.S.

⇒

⇒

⇒

⇒

⇒

⇒ cos A + sin A

⇒ L.H.S. = R.H.S.

Hence, Statement 1 is true.

Statement 2: (1 - sin A - cos A)2 = 2(1 - sin A)(1 + cos A)

Taking L.H.S.

⇒ (1 - sin A - cos A)²

⇒ [(1 - sin A) - cos A]²

⇒ (1 - sin A)² + cos²A - 2cos A(1 - sin A)

⇒ 1 + sin²A - 2sinA + cos²A - 2cosA(1 - sin A)

⇒ 1 + sin²A + cos²A - 2sin A - 2cos A(1 - sin A)

⇒ 2 - 2sin A - 2cos A(1 - sin A)

⇒ 2(1 - sin A) - 2cos A(1 - sin A)

⇒ 2(1 - sin A)(1 - cos A)

⇒ L.H.S. ≠ R.H.S.

Hence, Statement 2 is false.

∴ Statement 1 is true and Statement 2 is false.

Given:

α, β, γ are the zeroes of the polynomial f(x) = ax³ + bx² + cx + d.

Concept Used:

If α, β, γ are the zeroes of the cubic polynomial p(x) = ax³ + bx² + cx + d

Then,

Solution:

We have,

α, β, γ are the zeroes of the polynomial f(x) = ax³ + bx² + cx + d.

We have to calculate the value of

⇒

⇒  =

⇒  = {, }

⇒  =

Option 3 is correct.

Concept used:

One right-angle = 90°

Calculation:

⇒ ( - )

⇒ 8/3

So, 8/3 right-angles = 8/3 × 90 = 240°

∴ The correct answer is 240°

Given:

Difference between CI and SI = Rs. 50

Rate = 10%

Time = 2 years

Formula used:

CI – SI = P × (R/100)² for 2 years

where, P = Principal

R = Rate

Calculation:

According to question

We know that,

CI – SI = P × (R/100)²

⇒ P × (10/100)² = Rs. 50

⇒ P × (1/10)² = Rs. 50

⇒ P × (1/100) = Rs. 50

⇒ P = Rs. 5000

∴ The sum of money is Rs. 5000

Given:

The population of 7 villages is shown in the following pie chart.

If the total population of all the villages is 60000

Calculations:

According to the question,

Population of village G = 15% of total population of all villages

Population of G = 15% × 60000

Population of G = 0.15 × 60000 = 9000

∴ The population of village G is 9000.

Concept use:

Surface Area of Sphere = 4πr² where r is the radius of sphere

Volume of Sphere = 4/3 πr³ where r is the radius of sphere

Calculations:

The surface areas of two spheres are in the ratio 1 : 2.

4π(r₁)²/4π(r₂)² = 1/2

⇒ r₁²/r₂² = 1/2

⇒ r₁/r₂ = 1/√2

Volume of sphere 4/3 πr3

The Ratio of Volume of sphere = 4/3 πr₁3 / 4/3 πr₂3

⇒ r₁³/ r₂³ = 1: 2√2

Hence, The Correct Answer is 1: 2√2.

t² ‒ 2t ‒ 8 = 0
(t ‒ 4) (t + 2) = 0
t = 4 or ‒ 2

a² ‒ 4a ‒ 1 = 0
a = 2 ±√5

a² + 2a ‒ 1 = 0
a = ‒1 ± √2
Hence, option C is correct.

New student = 14 + 9 = 23
The average weight of new students

Hence, option C is correct.

From the figure, JP = 60 feet
∠JQP = 60°


Also, ∠JKP = 45°

∴ KP = 60
Required distance = KQ = KP – PQ

Hence, option A is correct.

When a container contains x quantity of liquid from which y units are taken out and replaced by water, after n operations, the quantity of pure liquid

Therefore, now milk in the container


Hence, Option A is correct.

2592 = 6 × 6 × 6 × 6 × 2


∴ We can easily see that, dividing 2592 by 12 gives us a perfect cube 216.
Hence, option (C) is correct.

In ΔCFB

In ΔCHI

CH = 2.5 cm
So, CG = 2.5 + 1.5 = 4 cm ---- (1)
In ΔCGE

GE = 3 cm (from eq. 1)

Hence, Option B is correct.

Reqd. Answer = 4 : (9 – 4) = 4 : 5
Hence, Option B is correct.

The pattern followed here is:

In all except option 3, each has circle inserted inside the other figure.

Hence, option 3 is the odd one.

As per the given information:

Seven friends P through V are sitting in a row facing north.

• P is sitting in the middle.
• S and T are sitting at alternate places with respect to P.

• Q and R are at the extreme ends.
• V is towards the right of U but not immediate right.

• S is to the immediate right of V

Case I will be eliminated as it contradicts given condition.

• Q is to the immediate right of S.

Clearly, T is sitting at second place from the left.

Hence, the correct answer is "T".

Given: Eight people - J, K, L, M, N, O, P, Q. All of them sitting in a straight line facing north.

Explanation:

Statement I: O is fourth to the right of L and 7th to the right of K.

So, according to the final arrangement of statement I, L is third to the right of K.

So, Only statement I, is sufficient to answer the question.

Statement II: Two person sit between K and L and K sits at extreme left end.

So, according to the final arrangement of statement II, L is third to the right of K.

So, Only statement II, is sufficient to answer the question.

Here, in both statements (I) and (II) L is sitting to the third right of K.

Thus either data in statement I or statement II is sufficient to answer the question.

Hence, the correct answer is 'Option 3'.

The Venn diagram is given below:-

Conclusions:

I. No introvert is an ambivert. → False (No introvert is an extrovert, all extroverts are ambiverts. So we can say that no introvert is an ambivert it can be possible but not definite, hence, false)

Il. No ambivert is an introvert. → False (No introvert is an extrovert, all extroverts are ambiverts. So we can say that no ambivert is an introvert it can be possible but not definite, hence, false)

III. Some ambiverts are extroverts. → True (All extroverts are ambiverts. So we can say that some ambiverts are extroverts as follow.)

IV. All ambiverts are extroverts. → False (All extroverts are ambiverts but all ambiverts are extroverts it does not follow.)

Hence, "option 3" is the correct answer.

The pattern followed is:

= Second number

= Third number

Let us check each option:

1. (400 – 40 – 4)

The pattern followed here is:

⇒ 400/10 = 40

⇒ 40/10 = 4

Then, it will be (400 – 40 – 4).

2. (300 – 30 – 7)

The pattern followed here is:

⇒ 300/10 = 30

⇒ 30 - 23 = 7

Then, it will be (300 – 30 – 7).

3. (1000 – 100 – 10)

The pattern followed here is:

⇒ 1000/10 = 100

⇒ 100/10 = 10

Then, it will be (1000 – 100 – 10)

4. (500 – 50 – 5)

The pattern followed here is:

⇒ 500/10 = 50

⇒ 50/10 = 5

Then, it will be (500 – 50 – 5).

The pattern followed is:

= Second number

= Third number

Option 1, Option 3 and Option 4 have the same pattern only Option 2 has a different one then, and the odd one out is Option 2.

Hence, the correct answer is 'Option 2'.

Given: Eight persons are sitting around a circular table facing the centre.

1) Z is second to the left of X.

2) U sits third to the left of X.

3) S is an immediate neighbour of both U and T.

4) Z is an immediate neighbour of both U and V.

5) W is an immediate neighbour of T.

6) Y sits second to the right of V.

So, 'X' sits third to the left of T.

Hence, the correct answer is "Option 4".

The set of letters which represents Indians who are either professors or fathers, is shown below:

Hence, ‘CEF’ is the correct answer.

The above PEOPLE is coded as OFNQKF
In word PEOPLE according to alphabetic order,
Steps decreased by 1 then P is coded by O
Steps increased by 1 then E is coded as F
Similarly O Steps decreased by 1 then coded as N
And P is coded as Q step increased by 1, likewise L E is coded as K F following the same pattern decreased by 1 and increased by 1, Similarly we code now SOCIETY by same combination of coding we get in place of S – R (step decreased by 1 per alphabetic order) and in place of O – P (step increased by 1 per alphabetic order) so we got the code of SOCIETY is RPBJDUX.

(13, 8, 3) has equal difference between each digit which is 5. So the same pattern is followed by option D. It also has equal difference of 4 between each digit. 
Hence, option D is correct.

From the word “ACCIDENTALLY”, if we take the second, sixth, eighth and twelfth letters of the word then the letters are C, E, T and Y respectively. As no meaningful English words can be formed, thus M would be the answer.

Hence, Option C is correct.

On close observation we get 'j' represents the kids watching Doraemon and Shinchan but not Chota Bheem.
Hence, option A is correct.

We may label the figure as shown.

The simplest triangles are IJO, BCJ, CDK, KQL, MLQ, GFM, GHN and NIO i.e. 8 in number.

The triangles composed of two components each are ABO, AHO, NIJ, IGP, ICP, DEQ, FEQ, KLM, LCP and LGP i.e. 10 in number. 

The triangles composed of four components each are HAB, DEF, LGI, GIC, ICL and CLG i.e. 6 in number. 

∴  Total number of trianngles in the figure = 8 + 10 + 6 = 24. 

Using the above information, we get the following diagram:

Alokit is in the North direction with respect to his initial position.
Hence, Option C is correct.