AD Practice DS SET -1
DS: Age & Digits – Level 1
Directions: Choose the correct option (A-E) based on sufficiency.
1.
What is John’s current age?
(1) Five years ago, John was 15 years old.
(2) In 10 years, John will be 30 years old.
(1) Five years ago, John was 15 years old.
(2) In 10 years, John will be 30 years old.
Solution (D):
(1) \( J – 5 = 15 \implies J = 20 \). Sufficient.
(2) \( J + 10 = 30 \implies J = 20 \). Sufficient.
2.
What is the two-digit number \( N \)?
(1) The sum of the digits of \( N \) is 9.
(2) The units digit is greater than the tens digit.
(1) The sum of the digits of \( N \) is 9.
(2) The units digit is greater than the tens digit.
Solution (E):
(1) Possible numbers: 18, 27, 36, 45, 54, 63, 72, 81, 90. Not sufficient.
(2) No specific numbers. Not sufficient.
Combined: From (1), numbers where units > tens are 18, 27, 36, 45. Still 4 possibilities. Not sufficient.
3.
Is the integer \( x \) divisible by 3?
(1) The sum of the digits of \( x \) is 12.
(2) The last digit of \( x \) is 3.
(1) The sum of the digits of \( x \) is 12.
(2) The last digit of \( x \) is 3.
Solution (A):
(1) A number is divisible by 3 if the sum of its digits is divisible by 3. Since 12 is divisible by 3, \( x \) is divisible by 3. Sufficient.
(2) Last digit 3 doesn’t guarantee divisibility by 3 (e.g., 13 is not divisible, 33 is). Not sufficient.
**Correction:** I labeled the answer as C in the prompt (accidentally). The correct answer is A. Statement (1) alone is the divisibility rule for 3.
3.
Is the integer \( x \) divisible by 3?
(1) The sum of the digits of \( x \) is 12.
(2) The last digit of \( x \) is 3.
(1) The sum of the digits of \( x \) is 12.
(2) The last digit of \( x \) is 3.
Solution (A):
(1) The rule for divisibility by 3 states that if the sum of digits is divisible by 3, the number is divisible by 3. 12 is divisible by 3, so YES. Sufficient.
(2) Having a last digit of 3 does not ensure divisibility (e.g., 13). Not sufficient.
4.
Who is older, Ann or Bob?
(1) Ann is 30 years old.
(2) The sum of their ages is 50.
(1) Ann is 30 years old.
(2) The sum of their ages is 50.
Solution (C):
(1) Gives Ann’s age. Don’t know Bob. Not sufficient.
(2) \( A + B = 50 \). Could be 25/25, or 40/10. Not sufficient.
Combined: \( A = 30 \). \( 30 + B = 50 \implies B = 20 \). Ann (30) > Bob (20). Sufficient.
5.
Is the tens digit of the two-digit number \( N \) odd?
(1) \( N > 50 \).
(2) \( N = 75 \).
(1) \( N > 50 \).
(2) \( N = 75 \).
Solution (B):
(1) \( N \) could be 60 (Tens 6, Even) or 70 (Tens 7, Odd). Not sufficient.
(2) \( N = 75 \). Tens digit is 7, which is Odd. Answer is definitive Yes. Sufficient.
Score: 0 / 0