Practice Questions
Concept Explanation
Number-based equations assign digits to variables and translate conditions about two-digit numbers, reversals, and digit sums into algebra.
Key Forms
- Two-digit number with tens digit a and units digit b: 10a + b
- Reversed number: 10b + a
- Digit sum: a + b
Example
A two-digit number is 27. Reversed is 72. Difference = 72 − 27 = 45 = 9 × (7 − 2).
Common Trap
Do not treat a two-digit number as a + b; place value matters: 10a + b.
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Q1 EasyWhen 15 is added to a certain number, the result is 42. What is that number?Explanationx + 15 = 42, so x = 27.
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Q2 EasyIn a two-digit number, the tens digit is 4 and the units digit is 7. What is the number?Explanation10 × 4 + 7 = 47.
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Q3 EasyWhat is the sum of the digits of the two-digit number 63?Explanation6 + 3 = 9.
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Q4 EasyA two-digit number is written as 10a + b, where a is the tens digit and b is the units digit. If the digits are reversed, which expression represents the new number?ExplanationReversal swaps place values: 10b + a.
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Q5 EasyOne number is 5 more than twice another number. If the smaller number is 6 and the larger is 17, what value does twice the smaller number plus 5 equal?Explanation2 × 6 + 5 = 17.
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Q6 EasyThree times a certain number increased by 7 equals 28. What is the value of that number?Explanation3x = 21, x = 7.
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Q7 EasyWhen a certain number is divided by 5, the quotient is 12. What is the original number?Explanationx/5 = 12, x = 60.
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Q8 MediumThe sum of a two-digit number and the number obtained by reversing its digits is 99. For the number with tens digit 5 and units digit 4, what is the sum of 54 and its reverse 45?Explanation54 + 45 = 99.
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Q9 MediumA two-digit number is greater than 50 and exceeds the number formed by reversing its digits by 27. Which of the following is the original number?ExplanationNumber − reverse = 9(a − b) = 27, so a − b = 3. With value above 50: 63 (− 36 = 27).
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Q10 MediumA certain positive number added to its square gives 72. Which number satisfies this condition?Explanation8 + 64 = 72.
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Q11 MediumWhen the number formed by reversing the digits of a two-digit number is subtracted from the original number then the result is 45. If the sum of the digits of the number is 9 then, what is the original number?Explanationx − y = 5 and x + y = 9 gives x = 7, y = 2. The number is 72.
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Q12 HardA two-digit number equals 9 times the sum of its digits. For the number 81, what is 81 divided by the sum of its digits (8 + 1)?Explanation81 ÷ 9 = 9.
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Q13 HardThe difference between a two-digit number and the number obtained by interchanging the position of its digit is 45. What is the difference between the two digits of that number?ExplanationNumber − reverse = 9(a − b) = 45, so a − b = 5.
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Q14 HardAfter a certain number is increased by 20%, it becomes 60. What was the original number?Explanation1.2x = 60, x = 50.
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DS1 Easy
What is the two-digit number whose tens digit is a and whose units digit is b?
Statement Ia = 5 and b = 4.
Statement IIThe number equals 10a + b.
ExplanationStatement I alone: 54. -
DS2 Easy
If twice a number plus 9 equals 31, what is the value of x?
Statement I2x = 22.
Statement IIx is a positive integer.
ExplanationStatement I alone: x = 11.
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DS3 Medium
What is the difference between a two-digit number and the number obtained by reversing its digits?
Statement IThe digits differ by 3.
Statement IIThe number is 63.
ExplanationEach alone: 63 − 36 = 27; or 9 × 3 = 27. -
DS4 Medium
Three consecutive integers add up to 54. What is the sum of those three integers?
Statement IThe middle integer is 18.
Statement IIThe integers are 17, 18, and 19.
ExplanationEach alone confirms the sum is 54.