The teacher explains, "Now take out your homework class, and answer these questions about the number you calculated for homework. Remember, it was a positive integer no more than 1000."

1 Is the number
A) Less than 100
B) Less than 900
C) Greater than 900

2 Is the sum of the digits
A) Greater than 10
B) Greater than 20
C) Greater than 30

3 Is the number divisible by:
A) 2
B) 3
C) 5

4 Are the digits:
A) Strictly increasing
B) Strictly decreasing

5 Is the number divisible by:
A) 15
B) 17
C) 19

6 If you get rid of the number's first digit, is it divisible by:
A) 19
B) 20

7 When spelled out, does the spelling use:
A) J
B) L
C) Q
D) V
E) X
F) Z

8 Ignoring the sign, what is the difference between the hundred's digit and the one's digit?
A) 2
B) 3
C) 4
D) 5

9) How many times does the letter E appear when the word is spelled out?
A) 3
B) 5
C) 7

10 Is the first digit of the number
A) Odd
B) Even

You panic, because you were too busy last night solving other things on flooble and didn't get a chance to do your homework. But when you figure out the quiz (where exactly one answer is right per question), you see that only one number will work.

What is this number?

(Note: Spelled out means in words. For example: 123 is "One hundred twenty three". Divisible means divided with no remainder. Also, padding the number with leading zeroes isn't allowed.)

You make a 100% on the quiz, that's what!

By the answers to #1, it can't be less than 100 because then it would also be less than 900, making 2 answers true. So the number is between 100 and 999, but NOT 900.

Looking at #2, the sum of the three digits CAN'T
begreater than 30, because 999 only totals to 27. Also, the number can't be greater than 20, because then it's also greater than 10, so the answer is between 11 and 20 inclusive. #2 is answer B.

By #5, the number is either div by 15,17,or 19. 17 and 19 are prime, but since #3 has both 5&3 as answers, it can't be both, ergo it CAN't be 15, so it's either a multiple of 17 or 19, but not both, i.e. NOT 323.

So listing out all multiples of 17 and 19 in a
spreadsheet seriously limits the solution set. Then going through these getting rid of those who dont' either ascend or descend leaves the folling possibilities.

Multiples of 17 (ascend or descend)
136,187,238,289,357,459,578,731,765,850,952,986

Multiples of 19 (ascend or descend)
247,456,532,589,741,760,874,931,950

Because of #6, you know that getting rid of the first digit leaves either a multiple of 19 or 20, but not both.

Only 60 (760) is divisible by 20. Multiples of 19 are 19,38,57,76,95 so the last 2 digits of the solution would have to be one of these. That leaves only 238 or 357.

So now we are down to three choices: 238, 357 or 760.

Therefore, #1 is B.

760 is a multiple of both 5 and 2, so that's out too.

Now it's 238 or 357, both of which ascend.

238 is divisible by 2 NOT 3, 357 is divisible by 3 NOT 2.

So C is NOT right for #3.

BOTH are multiples of 17, so #5 is B

Both of these are strictly increasing.
#6 is A, because these numbers are both div by 19.

Looking at #7:
TWO HUNDRED THIRTY EIGHT does NOT use any of those letters

THREE HUNDRED FIFTY SEVEN uses V, so #7 is D, and the answer is 357.

#8 The diff b/t 3 and 7 is 4, so C.

This also uses 5 E's. So does THREE FIVE SEVEN,
interestingly. So #9 is B

#10 is A, and # 3 is obviously B.

So the answers are
1 B
2 A
3 B
4 A
5 B
6 A
7 D
8 C
9 B
10 A

Posted by Lawrence on 2003-08-28 19:04:43