In the following number-pairs, the second number is obtained by applying certain mathematical operation(s) to the first number. Which numbers should replace X and Y, so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of ::?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 24 : : 13 : Y
Pattern Identification in Number Pairs
The question is based on a number analogy: A : B :: C : D. This format implies that the mathematical relationship between A and B is identical to the relationship between C and D.
In this case, the analogy is X : 24 :: 13 : Y.
Important Note: Operations must be performed on the entire numbers, not on their individual digits.
Deriving the Core Mathematical Operation
To solve this, we need to determine the operation that transforms the first number into the second.
Consider the relationship between 13 and Y, and X and 24. Based on the options and the typical nature of these problems, let's test the simplest operations. A common pattern is multiplication or addition.
If we test the option A (X=12, Y=26), we get the analogy: 12 : 24 :: 13 : 26.
- Left side: \(12 \times 2 = 24\).
- Right side: \(13 \times 2 = 26\).
The consistent mathematical operation is multiplying the first number by 2 to get the second number.
Calculating X and Y using the Pattern
We apply the identified pattern (Number \(\times\) 2 = Result) to find X and Y.
- For the pair X : 24: \(X \times 2 = 24\) Solving for X: \(X = \frac{24}{2}\) \(X = 12\)
- For the pair 13 : Y: \(13 \times 2 = Y\) \(Y = 26\)
Thus, X = 12 and Y = 26.
Confirming the Solution
The derived values complete the analogy as 12 : 24 :: 13 : 26, confirming that the pattern of multiplying by 2 holds true for both number pairs.
Similar Questions
Select the pair which follows the same pattern as that followed by the two set of pairs given below. Both pairs follow the same pattern.
ARH: YOJ
SFP: QCRFIGH is related to KNLM in a certain way based on the English alphabetical order. In the same way, RUST is related to WZXY. To which of the following options is HKIJ related, following the same logic?
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is same as that on the right side of ::? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) X : 179 :: 22 : Y
- Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of ::? # : EAG :: IEK : %
- Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 - Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(29, 116, 348)
(22, 88, 264) - MXEL is related to OZHP in a certain way based on the English alphabetical order. In the same way, VRHB is related to XTKF. To which of the given options is QOJA related, following the same logic?
- Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
3 – 9 – 81 – 66 ; 5 – 25 – 625 – 610 - Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(10, 5, 60)
(9, 6, 64) - Select the pair which follows the same pattern as that followed by the two pairs given below. Both pairs follow the same pattern.
FPD : ENB
RUN : QSL - Select the pair which follows the same pattern as that followed by the two pairs given below. Both pairs follow the same pattern.
KFM : GCR
RMS : NJX
Important Questions from Analogy
Select the option that is related to the third term in the same way as the second term is related to the first term.
Day: Night :: Morning : ?Select the option that is related to the third term in the same way as the second term is related to the first term.
India : Country :: Delhi : ..........Select the option that is related to the third term in the same way as the second term is related to the first term.
MATE: NATE :: FATE: ?Select the option that is related to the third term in the same way as the second term is related to the first term.
13 : 196 :: 9 : .......
Select the related word pair from the given alternatives. Afghanistan : Kabul :: ....... : .........
