Needgmat wrote:Kay began a certain game with x chips. On each of the next two plays, she lost one more than half the number of chips she had at the beginning of that play. If she had 5 chips remaining after her two plays, then x is in the interval
A) 7 <equal x <equal 12
B) 13<equal x <equal 18
C) 19<equal x <equal 24
D) 25<equal x <equal 30
E) 31<equal x <equal 35
OAD
Please explain.
Many thanks in advance.
Kavin
You could test the answer choices. If she loses one more than 1/2 of the original amount, we know that she must have started with an even number of chips, otherwise, we'd be dealing with non-integer values.
Try C. Pick an even number in the interval. Say x = 22. If she loses one more than 1/2 of her chips, she'll lose 11 + 1 = 12 chips, leaving her with 10 chips. If she has 10 chips to start round 2, and again, she loses one more than 1/2 of her chips, she'll lose 5 + 1 = 6 chips, leaving her with 4. But we know she has 5. (Notice that if you were to test another value in this interval and set x = 24, you'd end up with a non-integer value after the second round.)
So Try D. Say x = 26. If she loses one more than 1/2 of her chips, she'll lose 13 + 1 = 14 chips, leaving her with 12 chips. If she has 12 chips to start round 2, and again, she loses one more than 1/2 of her chips, she'll lose 6 + 1 = 7 chips, leaving her with 5. And so
D is our answer.
