CSAT Practice: Analogy - 3 - UPSC MCQ

14 = (2 x 9 - 4)

26 = (2 x 15 - 4)

? = 15

The logic follows here is :- 

The positional value of M is 13 and the positional value of O is 15. 

then , MO → 1315

Similarly,

The positional value of H is 8 and the positional value of J is 10.

then, HJ → 810

Hence, the correct answer is "810".

As, 123 → 13²

As, 235 → 25³

The middle digit of first term becomes power to the next term.

The logic is x³ : (x+1)³ + 1
                   2³ : (2 + 1)³ + 1
                   2³ : 3³ + 1
                   8  :  28
27 = 3³
so next digit (n+1)³ + 1 = (3 + 1)³ + 1 = 64 + 1 = 65

As position of M and N in Eq. alphabets are 13 and 14 respectively.Same position of F and R in Eq. alphabets are 6 and 18 respectively.

To solve the analogy problem where the pattern needs to be identified, let’s break it down step-by-step:

The analogy given is: 16 : 56 :: 32 : ?

We need to find the relationship between the numbers 16 and 56 and then apply that relationship to 32 to find the missing number.

1. Find the relationship between 16 and 56:

   • Step 1: Check the operations or patterns. Consider possible operations like addition, subtraction, multiplication, or division.

   • Step 2: Test if multiplication could be a pattern:

     16×3.5=56

     This works as:

     16×3.5=56

     Thus, multiplying by 3.5 seems to be the pattern.

2. Apply the same pattern to 32:

   32×3.5=112

   Therefore, according to this pattern, the number that replaces the question mark should be 112.

3. Verify the other options:

   • 96: This is much larger than expected.
   • 112: Also too large.
   • 121: Similarly, too large.
   • 128: While close, it’s not the result from our multiplication pattern.

Hence, the correct answer is:

112

As, (4)² + 3 = 19

Similarly, (7)² + 3 = 52

As 24:60 = (2/5)

Similarly, (120/300) = (2/5)

As 335 - 216 = 119

Similarly, 987 - X = 119

Therefore, X = 987 - 119 = 868.

24 → 2 x 4 = 8

32 → 3 x 2 = 6

Sure, let's find the correct answer for the given problem.

144 : 10 :: 169 : ?

- 144 is a perfect square (12²) and its square root is 12.
- 12 is then reduced to 10 by subtracting 2 (12 - 2 = 10).
- Similarly, 169 is a perfect square (13²) and its square root is 13.
- Following the same pattern, subtract 2 from 13 (13 - 2 = 11).

Thus, the correct answer is:

B: 11

- 169 : 11

9 = (3)²

8 = (3 - 1)³

and 16 = (4)²

? = (4 - 1)³ = 27

If we see diagonally we will get 11 22 31 and the next diagonal series is 12 21 32. Similarly the next diagonal series after 9 12 21 is 8 13 20.

As 25 = (5)² → (5 + 1)² + 1 = 37.

As 49 = (7)² → (7 + 1)² + 1 = 65.

In Eq. alphabets positions of K and T are 11 and 20 respectively.

Similarly positions of J and R are 10 and 18.

As, 68 = (4)³ + 4

    130 = (5)³ + 5

and 350 = (7)³ + 7

Therefore, ? = (6)³ + 6 = 222

As, 61 = (4)³ - 3

    121 = (5)³ - 4

and 337 = (7)³ - 6

Therefore, ? = (6)³ - 5 = 211