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Find the whole number that satisfies all of the following conditions.
• It is a whole number between 1 and 100 inclusive.
• 10% of the number is greater than 1 but less than 7.
of the number is a square number.
• The number is not a multiple of 6.
.
1/3

[3]
Note: Make your final answer clear by writing 'The number is ...'

User Woockashek
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1 Answer

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(the question is formatted a bit weird, but I'm assuming the third statement is meant to be '1/3 of the number is a square number'. If not, let me know and I'll adjust my answer accordingly)

Answer:

The number is 27

Explanation:

Let the number be called x.

10% of x is greater than 1 but less than 7. Written mathematically, this is 1<0.1x<7. Multiply this by ten to get 10<x<70.

1/3 of x is a square number. The squares 4, 9, and 16 are the only squares that satisfy this statement, because the if the square was 1, x would be 1, which doesn't fit x>10, and if the square was 25 or higher, x would be greater than 70, which doesn't fit x<70.

x isn't a multiple of six. If the square is 4, x is 12, which is a multiple of six so this doesn't work. If the square is 16, x is 48, which is a multiple of six too, so this doesn't work. But if the square is 9, x is 27, which isn't a multiple of six and satisfies the statement.

Double check that x=27 is a valid answer.

Is 27 a whole number between 1 and 100? Yes

Is 10% of 27 greater than 1 and less than 7? Yes (10% of 27 is 2.7)

Is 1/3 of 27 a square number? Yes (1/3 of 27 is 9, which is the square of 3)

Is 27 not a multiple of 6? Yes (27 isn't divided evenly by 6)

Therefore, the number is 27.

User Kumar Manglam
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