Search Previous Year Questions

Given: ‘ALPINE’ is coded as ‘171’ and ‘SPRING’ is coded as ‘83’. 

The logic follow here is: Addition of place value of given Letter × number of Vowel

 

Now, number of vowels = 3

= 57 × 3

= 171

And,

 

Now, number of vowels = 1

= 83 × 1

= 83

Similarly,

 

Now, number of vowels = 3

= 62 × 3

= 186

Hence, 186 is the correct answer.

In the following figure, we need to observe the 4 different kinds of patterns, which are running through each figure.​

• Pattern of circle 

: In the consecutive boxes the circle is transferred to the consecutive corner in a clockwise manner, Thus, in the following box the circle will be in the upper left corner.

​         

• Pattern of arrow 

: In each consecutive box, the direction of the arrow changes in an anticlockwise manner. Thus, in the following box, the arrow will face downwards.

​           

 

• Pattern of star 

: In each consecutive box, the star is moving diagonally upwards and then coming back to its origin diagonally. Thus, in the following box the star will be placed at the lower left corner.

​                

• Pattern of color: In consecutive boxes, one box has black colored star, whereas in the next box the arrow and circle are black colored. Thus, in the following box the star will be black colored, and the arrow and circle will not be colored.

​              

• Thus, the following box will contain the pattern made in Option 4.

  Hence, the correct answer is "Option 4".

The number of triangles in the given figure is:

Here, the number of triangles is '25'.

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

The logic followed here is :-

1. Vowels - Immediate previous letter according to English alphabetic series is written.
2. Consonants - Opposite letter according to English alphabetic series is written.

So,

• MAGIC is coded as :​

• FLUID is coded as :​

Similarly,

• HORSE is coded as :​

Hence, "SNIHD" is the correct answer.

The logic followed here is:

The middle letter is increasing by prime number order(2, 3, 5, 7).

​Hence, "UOQ" is the correct answer.

Given:

The ratio of monthly incomes of Radha and Rani is 3 : 2 and that their expenditure is 8 : 5 if each of them saves Rs. 9,000 per month

Formula used

Total Sum of the monthly incomes of Radha and Rani = Radha income + Rani income

Calculation

Let Income of Radha and Rani be 3x and 2x and Expenditure be 8y and 5y

Saving = 3x – 8y = 2x – 5y

⇒ x = 3y

According to the question, Saving = 9,000

⇒ 3x – 8y = 9,000

⇒ 3(3y) – 8y = 9,000

⇒ 9y – 8y = 9,000

⇒ y = 9,000

Then, total incomes of Radha and Rani = 5x = 5 × 3 × 9,000 = 1,35,000

Shortcut Trick

Let the two numbers be 9x and 9y, where x and y are co-prime.

Product of numbers = HCF × LCM ⇒ 9x × 9y = 9 × 252.

81xy = 2268 ⇒ xy = 28.

Possible co-prime pairs for xy = 28 are (1, 28) and (4, 7).

For (4, 7), Sum = 9 × (4 + 7) = 9 × 11 = 99.

∴ The correct answer is 99.

Alternate Method

Given:

HCF of two numbers = 9

LCM of two numbers = 252

Formula Used:

Product of two numbers = HCF × LCM

Calculations:

Let the numbers be a and b.

⇒ a = 9x and b = 9y (where HCF(x, y) = 1)

⇒ 9x × 9y = 9 × 252

⇒ 81xy = 2268

⇒ xy = 28

⇒ The factors of 28 that are co-prime are (4, 7).

⇒ x = 4 and y = 7

⇒ a = 9 × 4 = 36

⇒ b = 9 × 7 = 63

⇒ Sum = a + b = 36 + 63 = 99

∴ The correct answer is 99.

Additional Information

LCM and HCF Relationship

For any two numbers 'a' and 'b', a × b = HCF(a, b) × LCM(a, b).

HCF of Fractions

HCF = (HCF of Numerators) ÷ (LCM of Denominators).

LCM of Fractions

LCM = (LCM of Numerators) ÷ (HCF of Denominators).

Co-prime Property

Two numbers are co-prime if their Highest Common Factor is 1.

Given:

a - b = 4 and a³ - b³ = 88

Formula: ∴

(a³ - b³) = (a - b) (a² + b² + ab)

(a³ - b³) = (a - b) [(a - b)² + 3ab]

(a + b)² = a² + b² + 2ab

(a + b)(a - b) = a2 - b2

Calculation:

According to the formula

88 = 4 × (4² + 3ab)

⇒ 22 = 16 + 3ab

⇒ 3ab = 22 - 16

⇒ ab = 6/3

⇒ ab = 2

(a - b)² = a² + b² - 2ab

⇒ 4² = a² + b² - 2 × 2

⇒ a² + b² = 16 + 4 

⇒ a² + b² = 20

(a + b)² = 20 + 2 × 2

⇒ a + b = √24 = 2√6

Then (a + b)(a - b) = 2√6 × 4

⇒ 8√6 

∴ (a2 - b2) = 8√6

Shortcut Trick

Required number = LCM (10, 14, 12, 8) + Common Remainder

Prime factors of 10, 14, 12, 8 are used to find LCM.

LCM (10, 14, 12, 8) = 840

Required number = 840 + 7 = 847

∴ The correct answer is 847.

Alternate Method

Given: Divisors are 10, 14, 12, and 8. The remainder in each case is 7.

Formula Used: The least number which when divided by x, y, and z leaves the same remainder 'r' is (LCM of x, y, z) + r.

Step 1: Find the Prime Factorization of the given numbers:

⇒ 10 = 2 × 5

⇒ 14 = 2 × 7

⇒ 12 = 2² × 3

⇒ 8 = 2³

Step 2: Calculate the LCM (highest power of each factor):

⇒ LCM = 2³ × 3 × 5 × 7

⇒ LCM = 8 × 3 × 5 × 7 = 840

Step 3: Add the constant remainder to the LCM:

⇒ Required number = 840 + 7

⇒ Required number = 847

∴ The correct answer is 847.

Additional Information

LCM Property for Same Remainder

When a number leaves the same remainder r when divided by a, b, and c, the general form is N = k × LCM(a, b, c) + r, where k is an integer.

LCM Property for Different Remainders

If divisors are a, b, c and remainders are r₁, r₂, r₃ such that (a−r₁) = (b−r₂) = (c−r₃) = k, then the number is LCM(a, b, c) − k.

HCF vs LCM

HCF is the largest number that divides the given numbers, while LCM is the smallest number divisible by the given numbers.

Let the digit on one’s place be y and the digit in ten’s place be x

∴ The number is = 10x + y

Sum of the digits is 10

∴ x + y = 10

Now, when 18 is added, the digits are reversed

∴ New number = 10y + x

∴ (10x + y) + 18 = 10y + x

⇒ 9x + 18 = 9y

⇒ x + 2 = y

∴ x + y = 10

⇒ x + (x + 2) = 10

⇒ 2x + 2 = 10

⇒ 2x = 8

⇒ x = 4

∴ y = 10 – x = 10 – 4 = 6

∴ The number is 10x + y = (10 × 4) + 6 = 46

 

By option test, we can easily get the answer of the question.

From the given options only (4 + 6) = 10 and (3 + 7) = 10

So, our possible answer is either 46 or 37

Now, 37 + 18 = 55, which is not the number formed by changing the positions of the digits of the original number. So, it is also not our desire number.

Now, 46 + 18 = 64, which is the number formed by interchanging the positions of the digits of the original number.

∴ The desired answer is 46.