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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 the same as that on the right side of::? (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.) X:117::15:Y
X = 7, Y = 193
X = 9, Y = 195
X = 9, Y = 193
X = 7, Y = 195
X = 9, Y = 195
The pattern is (First Number * 13) = Second Number. Divide 117 by 13 to find X, and multiply 15 by 13 to find Y.
The pattern is (First Number * 13) = Second Number. Divide 117 by 13 to find X, and multiply 15 by 13 to find Y.
Analyze the existing pair
Looking at the right side of the analogy, 15 : Y. Based on the logic from the left side (X : 117), we check if 117 is a multiple of the common factors. 117 divided by 9 is 13.
Determine the rule
The relationship between the first and second number is: (First Number) * 13 = (Second Number). Applying this to 117: 117 / 13 = 9, so X = 9.
Calculate Y
Applying the same multiplier (13) to the right side: 15 * 13 = 195. Thus, Y = 195.
A: Incorrect; 7 * 13 = 91, not 117. C: Incorrect; X=9 is correct, but Y=193 is not 15 * 13. D: Incorrect; 7 * 13 = 91.
B is correct because the pattern follows the multiplication rule: First Number * 13 = Second Number, where 9 * 13 = 117 and 15 * 13 = 195.
In number analogy questions, always check for prime factors (like 13 here) if the difference between numbers is large.
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