A certain whole number less than 100 leaves the remainders 1,2,3, and 4 when divided, respectively by 2,3,4,and 5. What is the whole number?
2007-05-21 12:20:44 · 5 answers · asked by nadle88 1 in Science & Mathematics ➔ Mathematics
For this problem, you have to start with what you know.
x divided by 5 must have remainder of 4. With this piece of information, you know that it must have a ones digit value of 9 or 4.
x divided by 2 has a remainder of 1, so it must be odd. This leaves us that the ones digit must be 9 from the above.
From there, remove all numbers sub 100 that leave a remainder of 1 or 0 when divided by 3 (9, 19, 39, 49, 69, 79, 99).
This leaves you with possible candidates of 29, 59, and 89.
Only one of these numbers leave a remainder of 3 when divided by 4: 59. 29 and 89 both leave a remainder of 1.
The answer is 59.
2007-05-21 12:33:37 · answer #1 · answered by junkgolf 2 · 0⤊ 1⤋
the whole number is odd because if it is even, and divided by 2 it wont have a remainder. that narrows it down.it doesn't end with a 5 or a 0 because if divided by 5 it wont have a remainder.if you add the digits together and it equals something that 3 goes into than it isnt the correct whole number because it wont have a remainder when divided by 3. then you can do the hit-and-miss system and check through the most likely numbers. figure it out yourself so that you understand it better. the choices for the numbers are:::11,13,17,19,23,29,31,37,41,43,47,49,51,53,57,59,61, 67,69,71,73,77,79,83,87,89,91,97, or 100 i know it seems long but its full-proof. :) good luck!
2007-05-21 12:35:18 · answer #2 · answered by Anonymous · 0⤊ 1⤋
The answer is 59.
Eliminate all even numbers
Eliminate all numbers ending in 5
Eliminate all numbers that are a multiple of 3
From the numbers left, find all numbers that leave a remainder of 4 when divided by 5
Then chech to see if a remainder of 3 is left when divided by 4. ,etc
2007-05-21 12:38:22 · answer #3 · answered by ironduke8159 7 · 0⤊ 1⤋
The number is one greater than a multiple of two, so it is odd. Since it is also four greater than a multiple of five, it must end in a 4 or a 9... but it can only end in a nine in order to be odd. 9, 39, 69, and 99 can be quickly thrown out since they leave 0 when divided by 3. Only 29, 59, and 89 are two greater than a multiple of three. Of these, the only one that is three greater than a multiple of four is 59... so that is the answer!
2007-05-21 12:34:35 · answer #4 · answered by maree275 3 · 0⤊ 1⤋
This number plus one will go into 2,3,4 and 5,of which the smallest is 60. Thus the original number is 59.
2007-05-21 12:26:36 · answer #5 · answered by Michaelsgdec 5 · 0⤊ 0⤋