AD Practice SET – 2
Age & Digits: Level 2
1.
The ratio of the ages of Anna and Bob is 3:5. If the sum of their ages is 40, how old is Bob?
Solution (C):
Parts: \(3x + 5x = 40 \implies 8x = 40 \implies x = 5\).
Bob = \(5x = 5(5) = 25\).
2.
A number consists of two digits. The sum of the digits is 8. The tens digit is 2 more than the units digit. What is the number?
Solution (A):
Let number be \(10t + u\).
\(t + u = 8\).
\(t = u + 2\).
Substitute: \((u+2) + u = 8 \implies 2u = 6 \implies u = 3\).
\(t = 5\).
Number is 53.
3.
A mother is 3 times as old as her daughter. In 10 years, she will be twice as old as her daughter. How old is the daughter now?
Solution (D):
\(M = 3D\).
\(M + 10 = 2(D + 10)\).
Substitute: \(3D + 10 = 2D + 20 \implies D = 10\).
4.
If you add the digits of 199, what is the result?
Solution (B):
\( 1 + 9 + 9 = 19 \).
5.
Ben is 2 years younger than Dan. The sum of their ages is 30. How old is Dan?
Solution (E):
Let Dan = \(d\). Ben = \(d-2\).
\(d + (d-2) = 30 \implies 2d = 32 \implies d = 16\).
6.
What is the smallest 3-digit number whose digits sum to 4?
Solution (C):
To make it smallest, the hundreds digit must be minimal (1). The tens digit must be minimal (0). The remaining value goes to units (3).
Number = 103.
7.
The average age of 3 brothers is 15. The sum of the ages of two of them is 25. How old is the third brother?
Solution (A):
Sum of 3 ages = \(15 \times 3 = 45\).
Sum of 2 = 25.
Third = \(45 – 25 = 20\).
8.
If a number \(x\) has digits \(a\) and \(b\) (where \(x = 10a + b\)), what is the value of \(x\) if \(a=3\) and \(b=7\)?
Solution (B):
\(10(3) + 7 = 30 + 7 = 37\).
9.
Five years ago, the sum of ages of A and B was 40. What will be the sum of their ages 5 years from now?
Solution (D):
Let current ages be \(A\) and \(B\).
\((A-5) + (B-5) = 40 \implies A+B – 10 = 40 \implies A+B = 50\).
Future sum: \((A+5) + (B+5) = A+B+10 = 50+10 = 60\).
Alternatively: 5 years ago to 5 years future is a 10 year gap per person.
\(40 + 10 + 10 = 60\).
10.
In a 2-digit number, the units digit is 3 times the tens digit. If the sum of the digits is 12, what is the number?
Solution (C):
\(u = 3t\).
\(t + u = 12 \implies t + 3t = 12 \implies 4t = 12 \implies t = 3\).
\(u = 9\).
Number is 39.
Score: 0 / 0