AD Practice DS SET – 2
DS: Age & Digits – Level 2
1.
What is the two-digit number \( N \)?
(1) The tens digit is twice the units digit.
(2) The sum of the digits is 12.
(1) The tens digit is twice the units digit.
(2) The sum of the digits is 12.
Solution (C):
Let number be \( 10t + u \).
(1) \( t = 2u \). Possible numbers: 21, 42, 63, 84. Not sufficient.
(2) \( t + u = 12 \). Possible numbers: 39, 48, 57, 66, 75, 84, 93. Not sufficient.
Combined: From (1), \( t=2u \). Substitute into (2): \( 2u + u = 12 \implies 3u = 12 \implies u = 4 \). Then \( t = 8 \). Number is 84. Sufficient.
2.
How old is the father?
(1) The father is 3 times as old as his son.
(2) The sum of their ages is 60.
(1) The father is 3 times as old as his son.
(2) The sum of their ages is 60.
Solution (C):
(1) \( F = 3S \). Infinite possibilities.
(2) \( F + S = 60 \). Infinite possibilities.
Combined: \( 3S + S = 60 \implies 4S = 60 \implies S = 15 \). \( F = 45 \). Sufficient.
3.
Is the integer \( x \) odd?
(1) The sum of the digits of \( x \) is odd.
(2) \( x \) has 2 digits.
(1) The sum of the digits of \( x \) is odd.
(2) \( x \) has 2 digits.
Solution (E):
(1) Sum is odd. Example 1: \( 12 \) (Sum 3, Odd). Number 12 is Even.
Example 2: \( 23 \) (Sum 5, Odd). Number 23 is Odd.
Result can be Even or Odd. Not sufficient.
(2) Number of digits doesn’t tell parity. Not sufficient.
Combined: Same examples (12 and 23) are both 2-digit numbers with odd digit sums. Still not sufficient.
4.
What is the difference between Sue’s age and Fay’s age?
(1) Sue is 10 years older than Fay.
(2) 5 years ago, Sue was twice as old as Fay.
(1) Sue is 10 years older than Fay.
(2) 5 years ago, Sue was twice as old as Fay.
Solution (A):
(1) “Sue is 10 years older than Fay” directly gives the difference: \( S – F = 10 \). Sufficient.
(2) \( S-5 = 2(F-5) \). This equation has two unknowns and infinite solutions for the *difference* (depends on specific ages). Wait, let’s check.
\( S – 5 = 2F – 10 \implies S – 2F = -5 \).
Difference \( S – F = (2F – 5) – F = F – 5 \). The difference depends on Fay’s age. Not sufficient.
5.
Is the two-digit number \( N \) greater than 50?
(1) The tens digit is \( t \) and \( t > 4 \).
(2) The sum of the digits is 9.
(1) The tens digit is \( t \) and \( t > 4 \).
(2) The sum of the digits is 9.
Solution (A):
(1) Tens digit \( t \) can be 5, 6, 7, 8, 9.
Smallest number with \( t=5 \) is 50 (if digits 0-9 allowed). Question asks > 50.
If \( t=5 \), number is \( 50, 51 \dots \). 50 is not > 50.
But “two-digit number” usually implies positive integers.
If \( t=5 \), numbers are 50-59. 50 is not > 50.
If \( t > 5 \), numbers are > 60 (Yes).
Since \( t=5 \) yields a “No” for 50 and “Yes” for 51, this is Not Sufficient?
Wait, \( t > 4 \) means \( t \ge 5 \).
Let’s check (2). Sum is 9. Numbers: 18, 27, 36, 45, 54, 63, 72, 81, 90. Some < 50, some > 50. Not sufficient.
Combined: \( t \ge 5 \) AND sum=9.
Possible numbers: 54, 63, 72, 81, 90.
All these are greater than 50. Sufficient.
**Correction:** Wait, look at (1) again. If \(t \ge 5\), smallest is 50. Is 50 > 50? No. Is 51 > 50? Yes. (1) alone is NOT sufficient.
Combined is Sufficient. Answer is C.
Score: 0 / 0