Bunuel wrote:
Z = 578ab
Z is a positive integer whose ten-thousands digit is 5, thousands digit is 7, hundreds digit is 8, tens digit is a and units digit is b, as shown above. What is the value of a and b?
(1) The smallest number that must be subtracted from Z to make it divisible by 5 is 3
(2) The smallest number that must be added to Z to make it divisible by 4 is 1
Statement 1:To make it divisible by 5, the units digit needs to be 0 or 5. Since we need to subtract 3 to make it divisible by 5, we can tell the unit digit has to be 3 or 8. Insufficient.
Statement 2:We only need to check ab (the last two digits) to confirm if it is divisible by 4. With this information, ab can be any multiple of 4 minus 1 so insufficient. However, we may confirm the unit digit must be odd since in order to be divisible by 4 you need the number to be even first.
Combined:We know the unit digit must be 3. However, the tens digit can be 0, 2, 4, 6, or 8 so insufficient.
Ans: E
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