$$ \frac{49^2-35^2}{14}= $$

Question

$$\frac{49^2-35^2}{14}=$$ A. 74 B. 76 C. 78 D. 79 E. 84 The OA is the option E. Is there a fast way for solving this PS question without making the whole calculation? Please, I'd be thankful.

Vincen · Answer

Hello M7MBA.

Here, we have to use the following property $$a^2-b^2=\left(a+b\right)\left(a+b\right).$$ We have to susbtitute a=49 and b=35, then $$\frac{49^2-35^2}{14}=\frac{\left(49+35\right)\left(49-35\right)}{14}=\frac{84\cdot14}{14}=84.$$ This way we found the result without making a hard calculation.

Hence, the correct answer is the option E.

I hope it helps.

Brent@GMATPrepNow · Answer

M7MBA wrote:$$\frac{49^2-35^2}{14}=$$ A. 74
B. 76
C. 78
D. 79
E. 84

Vincen has demonstrated the approach I would have used. But, for "fun," here's another approach.

First, you need to know a nice trick for squaring numbers that end in 5 (the trick takes 2 minutes to learn, and then you can perform calculations like 65² and 35² in 5 seconds. Here's the video explaining this technique: https://www.gmatprepnow.com/module/gene ... video/1112)

So, using the technique, we know that 35² = 1225

For 49², let's estimate.
We know that 50² = 2500, so 49² must be a little less than 2500
Since 50² - 35² = 2500 - 1225 = 1225, we know that 49² - 35² will be a little less than 1225

So, we get: (49² - 35²)/14 = (a little less than 1225)/14
1125/14 = 87.5
So, (a little less than 1225)/14 = a little less than 87.5

Check the answer choices.....the correct answer must be E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Jeff@TargetTestPrep · Answer

M7MBA wrote:$$\frac{49^2-35^2}{14}=$$ A. 74 B. 76 C. 78 D. 79 E. 84 Simplifying we have: (49 + 35)(49 - 35)/14 (84 x 14)/14 = 84 Answer: E

M7MBA · Answer

Brent@GMATPrepNow wrote:M7MBA wrote:$$\frac{49^2-35^2}{14}=$$ A. 74 B. 76 C. 78 D. 79 E. 84 Vincen has demonstrated the approach I would have used. But, for "fun," here's another approach. First, you need to know a nice trick for squaring numbers that end in 5 (the trick takes 2 minutes to learn, and then you can perform calculations like 65² and 35² in 5 seconds. Here's the video explaining this technique: https://www.gmatprepnow.com/module/gene ... video/1112) So, using the technique, we know that 35² = 1225 For 49², let's estimate. We know that 50² = 2500, so 49² must be a little less than 2500 Since 50² - 35² = 2500 - 1225 = 1225, we know that 49² - 35² will be a little less than 1225 So, we get: (49² - 35²)/14 = (a little less than 1225)/14 1125/14 = 87.5 So, (a little less than 1225)/14 = a little less than 87.5 Check the answer choices.....the correct answer must be E Cheers, Brent Hi Brent@GMATPrepNow. Thanks for your solution. But the link you paste is for learning "how to divide by 5". Could you please send me the correct link? I want to learn this technique.

M7MBA · Answer

Brent@GMATPrepNow wrote:M7MBA wrote:$$\frac{49^2-35^2}{14}=$$ A. 74 B. 76 C. 78 D. 79 E. 84 Vincen has demonstrated the approach I would have used. But, for "fun," here's another approach. First, you need to know a nice trick for squaring numbers that end in 5 (the trick takes 2 minutes to learn, and then you can perform calculations like 65² and 35² in 5 seconds. Here's the video explaining this technique: https://www.gmatprepnow.com/module/gene ... video/1112) So, using the technique, we know that 35² = 1225 For 49², let's estimate. We know that 50² = 2500, so 49² must be a little less than 2500 Since 50² - 35² = 2500 - 1225 = 1225, we know that 49² - 35² will be a little less than 1225 So, we get: (49² - 35²)/14 = (a little less than 1225)/14 1125/14 = 87.5 So, (a little less than 1225)/14 = a little less than 87.5 Check the answer choices.....the correct answer must be E Cheers, Brent Hi Brent@GMATPrepNow. Thanks for your solution. But the link you paste is for learning "how to divide by 5". Could you please send me the correct link? I want to learn this technique.

Brent@GMATPrepNow · Answer

M7MBA wrote:
Hi Brent@GMATPrepNow.

Thanks for your solution.

But the link you paste is for learning "how to divide by 5". Could you please send me the correct link? I want to learn this technique.

My bad.
Here's the video for squaring numbers that end in 5: https://www.gmatprepnow.com/module/gmat ... video/1024

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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