Let the numbers be 27a and 27b
27a + 27 b =216
a + b =216/27=8
Co-primes of 8 are (1,7) and (3,5)
numbers=(27 * 1 ), (27 * 7)
=27,89
HCF concept question
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Stuart@KaplanGMAT
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The 4th Step of the Kaplan method for Problem Solving is to confirm that your answer makes sense.eaakbari wrote:Let the numbers be 27a and 27b
27a + 27 b =216
a + b =216/27=8
Co-primes of 8 are (1,7) and (3,5)
numbers=(27 * 1 ), (27 * 7)
=27,89
Does 27 + 89 = 216? No - therefore your solution is incorrect.
The problem with your solution is that you took 1 as a prime number, which it's not. Another problem is that you've calculated 7*27 as 89, which it's certainly not. If you're defining co-primes as "two numbers that don't share any factors", then 3/5 is the only choice in this question.
Let's go back to the beginning:
If the greatest common factor of the numbers is 27 (as an FYI, you'll never see shortforms like "HCF" on the GMAT, which makes me supremely sceptical of the mysterious source of this question, unless the author is paraphrasing the text), then we can certainly copy your first step and say that our two numbers are:
27a and 27b, in which a and b are integers.
So, as you noted:
27a + 27b = 216
27 (a+b) = 216
a + b = 216/27 = 8
So, we're looking for two multiples of 27 whose coefficients (i.e. the number of times we're multiplying them by 27) add up to 8.
However, we have another restriction: the numbers can't have any factors in common. Looking at the pairs of numbers that add up to 8:
1/7
2/6
3/5
4/4
the only pair without any common factors is 3 and 5.
So, our two numbers must be:
3(27) = 81
and
5(27) = 135
Finally, a quick confirmation:
81 + 135 = 216... bingo!
A prep book for what? A prep book for the GMAT should include choices, unless you're just working on math drills. What's the exact source?No choices as its from a prep book
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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