Lesson: General GMAT Math Strategies

Comment on General GMAT Math Strategies

GMAT practice question (difficulty level: 650 to 800) – Veritas Prep--- this is a good question!
gmat-admin's picture

I agree. Lots of different ways to solve that question.

I did not understand how you have arrived at the final answer. I only got the total sum as 6105 following the method given in the video. i.e (110-1)+1= 55 pairs sum of 111= 6105
gmat-admin's picture

Question link: https://gmatclub.com/forum/the-sum-of-the-digits-used-to-write-the-sum-1...

You're correct to say that 1 + 2 + 3 + . . . + 109 + 110 = 6105, but this is not what the question is asking.

The question asks you to find the sum of the DIGITS of the numbers from 1 to 110.

For example, 203 + 561 = 764

However, the sum of the DIGITS = 2 + 0 + 3 + 5 + 6 + 1 = 17


If I do not know how many pairs of 65, but I know for sure that the fourth digital of their sum must be 0 or 5, so the only choice E 1365.
gmat-admin's picture

Perfect reasoning!

Hello Brent,

Can you help with the following question please! Thanks

(-1.9)(0.6) – (2.6)(1.2))/6.0 = ?

A) -0.71

B) 1.00

C) 1.07

D) 1.71

E) 2.71
gmat-admin's picture

You bet!

We can apply the halving-doubling strategy (explained here: https://www.gmatprepnow.com/module/general-gmat-strategies/video/1113)

Let's deal with the NUMERATOR first.

Applying the halving-doubling strategy, we can write the following:
(2.6)(1.2) = (5.2)(0.6)

So, we get: (-1.9)(0.6) – (2.6)(1.2) = (-1.9)(0.6) – (5.2)(0.6)
= 0.6(-1.9 - 5.2) [I factored out the 0.6]
= 0.6(-7.1)

(-1.9)(0.6) – (2.6)(1.2))/6.0 = (0.6)(-7.1)/(6.0)
= (0.6/6.0)(-7.1)
= (1/10)(-7.1)
= -0.71


gmat-admin's picture

Now comes the 10-second solution!

When we scan the answer choices (ALWAYS scan the answer choice before performing any calculations), we see that only one answer choice is NEGATIVE (hmmmm!!!)

In the numerator we have: (-1.9)(0.6) – (2.6)(1.2)
(-1.9)(0.6) is NEGATIVE
And (2.6)(1.2) is POSITIVE

So, (-1.9)(0.6) – (2.6)(1.2) = NEGATIVE - POSITIVE
So, the numerator is some NEGATIVE number

The denominator (6) is a POSITIVE number

So, the entire fraction becomes NEGATIVE/POSITIVE, which evaluates to be NEGATIVE.
In other words, the entire fraction has a NEGATIVE value

Since answer choice A is the only NEGATIVE answer choice, it must be the correct answer.


Thank you so much. this video makes me feel relieved :)

gmat-admin's picture

Glad to hear that!

For 65x21, I noticed that anytime 65 is multiplied by an odd number you will have 5 in the unit field. Is this property explained later in the arithmetic section? Even though lengthy calculations can be avoided, I still feel like it's important to learn addition, multiplication, and division by hand. I guess I have to look up my notes from 2nd grade lol
gmat-admin's picture

Good observation.

If k is an integer, then 65k will have EITHER units digit 0 OR units digit 5.
Since ODD x ODD = ODD, we know that 65 x 21 will be ODD, which means it must have units digit 5.
This is covered here: https://www.gmatprepnow.com/module/gmat-integer-properties/video/837

Alternatively, we can apply something called the distributive property to explain your findings.
(65)(21) = 65(20 + 1)
= 65(20) + 65(1)
= 1300 + 65
= 1365
This property is covered here: https://www.gmatprepnow.com/module/gmat-arithmetic/video/1057


Hi Brent,

I've been looking for an accurate breakdown on topics on the quant section and found this post: https://gmatclub.com/forum/overview-of-gmat-math-question-types-and-patterns-on-the-gmat-211809.html

Do you know if this breakdown of the quant section is up to date/still relevant for the GMAT in 2019?
gmat-admin's picture

Link: https://gmatclub.com/forum/overview-of-gmat-math-question-types-and-patt...

I'm not sure what source the author used to create that table, but I think it's pretty accurate (based on what I've heard from students who have taken the test recently). I'd say that Integer Properties questions (remainders, divisibility, etc) aren't quite as high as 30% (maybe more like 15-20%). I'd also say that overlapping sets, percents and ratios are tested more than the table suggests.


Hi Brent,

When doing problem solving and data sufficiency problems, is ALL the given info going to be relevant/necessary to solve the problem? I have found that when doing quant problems, I have mostly had to use every piece of given information (in the problem itself, not the statements in DS) in order to solve the problem. I wanted to know if this is a general rule of thumb.

gmat-admin's picture

There are some examples of the given information including useless information (i.e., information that doesn't help us determine the sufficiency of either statement), but these instances are pretty rare.

1. Are the Math questions equally spread to cover all concepts such as Arithmetic (number properties, etc.), Algebra, and Geometry?

2. What, if any, formulas and math concepts do I need to memorize that would be helpful on test day? If I could only memorize a max of 10 (I have a poor memory), which would these be?

Thank you!
gmat-admin's picture

1. Some concepts are tested often while other concepts are rarely tested.
In general, the number of reinforcement questions beneath each video lesson is directly proportional to how often those concepts are tested,
So, for example, there are TONS of practice questions beneath the inequalities lesson (https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...), which means this is a frequently-tested concept.
Conversely, there are only a handful of practice questions beneath the quadratic inequalities lesson (https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...), which means this concept is rarely tested.

2. The answer to this question is related to my response to the first question. So, be sure to memorize the formulas related to frequently-tested concepts.

On a related note, you can download my GMAT math flashcards here: https://www.gmatprepnow.com/content/free-content


Thank you so much for this information - very helpful!
Yulia's picture

Question 1: https://gmatclub.com/forum/when-running-a-mile-during-a-recent-track-meet-nuria-was-initially-214040.html
How did you estimate that 11/25 is about 1/2? I would probably estimate like that 10/25= 2/5= 20 secs.

Question 2: https://gmatclub.com/forum/1-167461.html
How do you know how to round a number? [(-1.5)(1.2) - (4.5)(0.4)]/30 ≈ [(-2)(1) - (4)(0.5)]/30
Why (-1.5)(1.2) is rounded to (-2)(1) and (4.5)(0.4) to (4)(0.5)? I rounded it like (-2)(1)-(5)(1). I got the answer correct but still struggling with proper rounding. However, I understand how to round number. For instance 4.5 rounded to the whole number is 5, or 0.00096 rounded to 0.001. What am I missing in this question?

Question 3: https://gmatclub.com/forum/79-laboratories-raise-the-bacterium-the-laboratory-have-48-culture-di-214580.html
Is this approach work? 25,000 x 50= 1.25 x 10^6 while 79 = 8 x 10; 1.25 x 10^6 x 8 x 10= 1.25 x 8 x 10^7= 10 x 10^7 = 10^8
gmat-admin's picture

QUESTION #1: https://gmatclub.com/forum/when-running-a-mile-during-a-recent-track-mee...
We know that 12.5/25 = 1/2, so 11/25 will be a little bit less than 1/2.

It's important to note that your estimation has the same results as my estimation.
If we add your 20 seconds to 5 minutes 44 seconds, we get over 6 minutes. So the answer is still E.

QUESTION #2: https://gmatclub.com/forum/1-167461.html
Since the answer choices are quite spread apart (relatively speaking), we can be pretty aggressive with our estimation.
When estimating a product of two numbers, it's good practice to round one number UP and the other number DOWN. This will minimize the margin of error.
So, with (-1.5)(1.2), I rounded 1.5 UP to 2, and rounded 1.2 DOWN to 1.
Likewise, with (4.5)(0.4), I rounded 4.5 DOWN to 4, and rounded 0.4 UP to 0.5

You're not missing anything. Notice that, for Question #1, your estimation still yielded the correct answer.
Likewise, for Question #2, we can estimate in a variety of ways and still get the answer correct.
For example,
[(-1.5)(1.2) - (4.5)(0.4)]/30 ≈ [(-1)(1) - (5)(0.5)]/30 ≈ (-3.5)/30
Since our result is negative, we can eliminate answer choices D and E.
Also since our result is not 0, we can eliminate C.
Finally, (-3.5)/30 is much closer to -0.12 than it is to -1.2
So the correct answer is still B

QUESTION #3: https://gmatclub.com/forum/79-laboratories-raise-the-bacterium-the-labor...
Your approach is perfect.
Nice work!!


Yulia's picture

Thank you Brent. :-)

Official vs Unofficial

While practicing Quantitative topics, be sure to practice with both official and unofficial questions.

Scoring Algorithm

The GMAT scoring algorithm penalizes you much more for getting easy questions wrong than it rewards you for getting difficult questions right. So, it’s better to guess on hard questions so you’ll have enough time to answer easier questions.

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