In the following number-pairs, the second number is obtained by applying…
2025
In the following number-pairs, the second number is obtained by applying certain
mathematical operation(s) to the first number. Select the number-pair in which the
numbers are related in the same way as are the numbers of the following pairs.
(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.)
17,75
14,60
- A.
21,95
- B.
12, 80
- C.
19, 105
- D.
18, 90
Show answer & explanation
Correct answer: A
A number-pair analogy is governed by a single fixed rule of the form (first number × a) + b, where a and b are constants that convert every given pair’s first number into its second number. When the ratio between the two numbers is not the same across the given pairs, the rule cannot be pure multiplication — it must be recovered by solving two simultaneous linear equations for a and b, and that same rule then applies to the pair being matched.
Let the rule be: second number = a × (first number) + b.
From the first given pair (17, 75): 17a + b = 75.
From the second given pair (14, 60): 14a + b = 60.
Subtracting the two equations eliminates b: (17a + b) − (14a + b) = 75 − 60, so 3a = 15, giving a = 5.
Substituting a = 5 into 17a + b = 75: 85 + b = 75, so b = −10.
The rule for this pair-set is therefore: second number = (first number × 5) − 10.
Apply this rule to the first number of each option and compare the result with that option’s own second number.
First number | Rule output (5 × n) − 10 | Given second number |
|---|---|---|
21 | 5 × 21 − 10 = 95 | 95 |
12 | 5 × 12 − 10 = 50 | 80 |
19 | 5 × 19 − 10 = 85 | 105 |
18 | 5 × 18 − 10 = 80 | 90 |
As an independent check, reversing the rule on 95 gives (95 + 10) ÷ 5 = 21, which matches the first number of that pair — confirming the rule both forward and backward.
Only the pair 21, 95 satisfies the rule 5 × (first number) − 10 = second number, the same rule that connects 17 to 75 and 14 to 60. Hence the number-pair 21, 95 is related in the same way as the two given pairs.