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LCM of 32 and 40 = 160.

According to the given condition: X² − 9 = 160.

Adding 9 to both sides: X² = 169.

Taking square root: X = 13.

∴ The correct answer is 13.

Alternate Method

Given:

Numbers = 32 and 40.

Condition: LCM(32, 40) = X² − 9.

Step-by-step Calculation:

⇒ Prime factorization of 32 = 2 × 2 × 2 × 2 × 2 = 2⁵.

⇒ Prime factorization of 40 = 2 × 2 × 2 × 5 = 2³ × 5.

⇒ LCM (32, 40) = Highest power of all factors = 2⁵ × 5 = 32 × 5 = 160.

⇒ According to the problem: 160 = X² − 9.

⇒ X² = 160 + 9.

⇒ X² = 169.

⇒ X = √169.

⇒ X = 13 (Taking positive value as required).

∴ The correct answer is 13.

Additional Information

Least Common Multiple (LCM)

The LCM of two or more numbers is the smallest positive integer that is perfectly divisible by each of the given numbers.

Perfect Squares

A perfect square is an integer that is the square of an integer; for example, 169 is a perfect square because it equals 13².

Relationship between LCM and HCF

For any two positive integers a and b, the relationship is: LCM(a, b) × HCF(a, b) = a × b.

Given: 

The total price of all these 6 articles is 5040.

Concept Used:

All slices of the pie chart add up to make the whole equal 100 percent or 360 degrees.

Calculation:

For statement I:

The total price of A1 = 32°/360° ×  5040 = 448

The total price of A2 = 46°/360° × 5040 = 644

The total price of A4 = 50°/360° × 5040 = 700

The total price of A6 = 70°/360° × 5040 = 980

The total price of A1, A2, A4 and A6 = 448 + 644 + 700 + 980

= 2772

So, Statement I is correct.

For statement II:

The total price of A3 = 132°/360° × 5040 = 1848

The total price of A5 = 30°/360° × 5040 = 420

The total price of A4 = 50°/360° × 5040 = 700

The total price of A6 = 70°/360° × 5040 = 980

The total price of A3 and A5 together = 1848 + 420

= 2268

The total price of A4 and A6 together = 980 + 700

= 1680

The difference between the total price of A3 and A5 together and the total price of A4 and A6 together

= 2268 - 1680

= 588

So, Statement II is not correct.

Only statement II is not correct.

Given:

675.456 + 12.492 × 55.671 = ?

Calculation :

Let the unknown number be x.

⇒ 675.456 + 12.492 × 55.671 = x 

⇒ 675.5 + 12.5 × 55.5 = x         (55.671 ≈ 55.5)

⇒ 675.5 + 693.75 = x  

⇒x = 1369.25 ≈ 1371

∴ Option (4) is the correct answer.

Calculation:

The angle formed by sectors A, B and C together is  (13 + 24 +18) = 55%

The central angle formed by sectors E, F and G together is (7 + 4 + 15) = 26%

The difference is 55 - 26 = 29%

As per the question,

Value of 100% is 360° 

So, value of 29% will be 29 × 3.6 = 104.4° 

∴ The correct option is 3

Calculation:

Area of square room

= (10)2 = 100 sq m = 100 × (100)2 sq cm

= 100 × 100 × 100 sq cm

Now, area of tile

= (50)2 = 50 × 50 sq cm

∴ Number of tiles needed

$= \frac{{Area;of;square;room}}{{Area;of;tile}}$

$= \frac{{100 \times 100 \times 100}}{{50 \times 50}} = 400$

The pattern followed here is:

Logic: (1^st number + 1)² = 2^nd number.

So, 8 : 81

→ (8 + 1)² = 9² = 81.

Similarly, ? : 64

→ (7 + 1)2 = 82 = 64.

Hence, the correct answer is "Option 3".

The logic followed here is :-

Hence, the correct answer is "ECG".

The logic followed here is:

1) E is older than only A and B

⇒ E > A and B

2) D is younger than only C

⇒ C > D > E > A and B

3) A is not the youngest.

So, the correct order will be ⇒ C > D > E > A > B

So, there are 3 persons (C, D, and E) older than A.

Hence, "option 3" is the correct answer.

Given:

MPT, PRU, STV, VVW,?

Logic: Addition of (3), (2) and (1) in the position value of the first, second and third letter.

Here, 'YXX' is the next term.

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

Given Statements:

All tables are strong.

No strong is weak.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No tables are weak - True (Because, All the tables are strong and no strong is weak, so no tables are weak).

II. Some weak are tables - False (Because, All the tables are strong and no strong is weak, so no tables are weak).

So, Only conclusion I follows.

Hence, the correct answer is "Option 4".