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Number Properties: Tips and hints

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Bunuel

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01 May 2020, 10:31

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Bunuel

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Bunuel

Number Properties: Tips and hints

PERFECT SQUARES
1. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square;
2. The sum of distinct factors of a perfect square is ALWAYS ODD. The reverse is NOT always true: a number may have the odd sum of its distinct factors and not be a perfect square. For example: 2, 8, 18 or 50;

According to (1) and (2)
36 has ODD number of distinct factors...
but discrinct factors of 36 are 2 and 3
i.e. TWO factors i.e. EVEN.
Please explain..

Also, if you are going to include 1 in the list, it makes statement (2) Flawed!!
Because
(A) 1 + 2 + 3 = 6 = Even ≠ Odd

Shouldn't statement (1) use the term Distinct Prime factors?

I'm confused!

Factors of 36 are 1 | 2 | 3 | 4 | 6 | 9 | 12 | 18 | 36 (9 divisors).
Odd factors of 36 are 1, 3, and 9.
Even factors of 36 are 2, 4, 6, 12, 18, and 26.
Prime factors of 36 are 2 and 3: 36 = 2^2*3^2.

Hi, thanks for the response.
Just to clear things out,
The term “Distinct Factors” means all the Integers that are part of the Set of factors, whether prime or not.
Right?

I think I was unnecessarily confusing myself between distinct factors and distinct prime factors.
Thanks

Yes, prime factors and factors are not the same. For example, factors of 6 are 1, 2, 3, and 6. While prime factors of 6 are 2 and 3.

CEdward

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Updated on: 23 Nov 2020, 12:59

Originally posted by CEdward on 23 Nov 2020, 12:54.
Last edited by CEdward on 23 Nov 2020, 12:59, edited 1 time in total.

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bazc

Another tip,

If B is 1/x times more than A, then A is 1/(x+1) times lesser than B.

This is especially useful in averages, profit and loss, time rate questions.

Example:

If B's wage is 25% more than A's wage, then what is A's wage in terms of B?

B is 1/4 times more than A, so A will be 1/5 or 20% lesser than B. i.e., A = 80% of B

On test day people (including myself) might scramble and forget formulas. Would a solution like so work just as well?

B = (5/4)A --> A = (4/5)B

bazc

Tip for questions involving recurring decimals:

Note the following pattern for repeating decimals:
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999

Note the pattern if zeroes preceed the repeating decimal:
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900

Are there other such patterns for repeating decimals for divisibility involving non 9? What about example questions where this might become relevant?

ruis

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20 Feb 2024, 06:34

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Any tip / hint on Conversion problems? I usually mess up there! It takes me 4 mins on average to do exercises of this type... I keep practicing to become better but any tip would help a lot!

Thanks!

Bunuel

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20 Feb 2024, 09:56

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ruis

:) Thanks!

Check out Conversion problems to practice from our Special Questions Directory.

Also, the links below should help with arithemtic:

How to Do Math on the GMAT Without Actually Doing Math
The Power of Estimation for GMAT Quant
How to Plug in Numbers on GMAT Math Questions
Number Sense for the GMAT
Can You Use a Calculator on the GMAT?
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT

Hope it helps.

ruis

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20 Feb 2024, 10:02

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Bunuel

ruis

:) Thanks!

I am learning more on GMAT Club than I ever did at school. Thank you really for everything. Maths has always been a lack of confidence for me and I am starting to gain confidence for the first time

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19 Mar 2025, 07:51

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ruis

Bunuel

ruis

:) Thanks!

I am learning more on GMAT Club than I ever did at school. Thank you really for everything. Maths has always been a lack of confidence for me and I am starting to gain confidence for the first time

thought I was the only one

(was okay at maths, good if i put effort, but Gmat Club and the whole Gmat prep experience in general has been amazing for improving my maths skills)

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05 Apr 2026, 04:02

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Bunuel

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