Using GMAT Divisibility Rules to Answer Quant Questions Faster
As we learned in a previous blog, the GMAT does not allow a calculator in the Quant section. Thus, it’s important to memorize and be able to use divisibility rules in answering certain questions.
There are times when these divisibility rules can be helpful in simplifying numbers and prime factorization, and times when these rules can be helpful in determining whether a number is a multiple of another number.
Before diving into specific examples, let’s review the divisibility rules for 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
GMAT Divisibility Rules: An Overview
Number Divisible by 0
No number is divisible by 0.
Number Divisible by 2
A number is divisible by 2 if the ones digit is 0, 2, 4, 6, or 8 – that is, if the units digit is even.
For example, 30, 42, 54, 66, and 78 are divisible by 2.
Number Divisible by 3
A number is divisible by 3 if the sum of all the digits is divisible by 3.
For example, 472,071 is divisible by 3 because the sum of its digits (4 + 7 + 2 + 0 + 7 + 1 = 21) is divisible by 3.
Number Divisible by 4
If the last two digits of a number are divisible by 4, then the number is divisible by 4.
For example, the last two digits of 244 are 44, which is divisible by 4. Students sometimes fail to see that a number that ends in 00 is divisible by 4. Just remember that all multiples of 100 are divisible by 4, since 100 = 25 x 4.
Number Divisible by 5
A number is divisible by 5 if the last (ones) digit is 0 or 5.
For example, the numbers 55 and 70 are divisible by 5.
Number Divisible by 6
A number is divisible by 6 if the number in question is an even number whose digits sum to a multiple of 3 (and therefore the number is divisible by both 2 and 3, the factors of 6).
For example, 18 is an even number, and its digits, 1 and 8, sum to 9, a multiple of 3.
Number Divisible by 7
There are tricky formulas for this, but their logic is complicated. So, if you are asked whether a number is divisible by 7, just do the division.
Number Divisible by 8
If the number is even, divide the last three digits by 8. If there is no remainder, then the original number is divisible by 8.
For example, the number 1,160 is divisible by 8 because 160/8 = 20, which is an integer. Students often fail to see that if a number ends in 000, the number is divisible by 8. Just remember that all multiples of 1,000 are divisible by 8 because 1000 = 125 x 8.
Number Divisible by 9
A number is divisible by 9 if the sum of all the digits is divisible by 9.
For example, 479,655 is divisible by 9 because the sum of the digits (4 + 7 + 9 + 6 + 5 + 5 = 36) is divisible by 9.
Number Divisible by 10
If the ones digit is 0, then the number is divisible by 10.
For example, 10, 80, 90, 100, 1,120, and 10,000 are all divisible by 10.
Number Divisible by 11
A number is divisible by 11 if the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11. The odd-numbered place digits are the 1st, 3rd, 5th, and so on digits to the left of the decimal point. Hence, they are the ones, hundreds, ten-thousands, and so on digits. Similarly, the even-numbered place digits are the 2nd, 4th, 6th, and so on digits to the left of the decimal point. Hence, they are the tens, thousands, hundred-thousands, and so on digits.
For example, 253 is divisible by 11 because (2 + 3) – 5 = 0, which is divisible by 11 (remember, 0 is divisible by any number except itself). Likewise, 2,915 is divisible by 11 because (9 + 5) – (2 + 1) = 11, which is divisible by 11.
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