2ab5 is a four digit number divisible by 25. If a number formed from the two…
2023
2ab5 is a four digit number divisible by 25. If a number formed from the two digits ab is a multiple of 13 , then ab is
- A.
65
- B.
75
- C.
52
- D.
25
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Correct answer: C
Answer: 52
Key insight: A number is divisible by 25 only if its last two digits are 00, 25, 50, or 75.
For the four-digit number 2ab5 the last two digits are b5. From the allowed endings, b5 can be 25 or 75, so b must be 2 or 7.
The two-digit number ab must be a multiple of 13. The two-digit multiples of 13 are: 13, 26, 39, 52, 65, 78, 91.
Combine both conditions: b must be 2 or 7, so among the multiples above only 52 has b = 2 (and 78 has b = 8, 65 has b = 5, etc.). Therefore 52 is the only multiple of 13 that also gives b = 2 or 7.
Thus ab = 52, because b = 2 makes the last two digits 25 (giving divisibility by 25) and 52 is divisible by 13.