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Sub 505 (Easy)|   Arithmetic|   Exponents|      
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adkikani
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(49^2 - 35^2)/14 = Updated on: 10 Dec 2017, 20:52
Originally posted by adkikani on 10 Dec 2017, 18:51.
Last edited by Bunuel on 10 Dec 2017, 20:52, edited 1 time in total.
Renamed the topic, edited the question
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

87% (01:15) correct 13% (02:33) wrong based on 351 sessions

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\(\frac{(49^2 - 35^2)}{14} =\)

A. 74
B. 76
C. 78
D. 79
E. 84
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E
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(49^2 - 35^2)/14 = 10 Dec 2017, 19:03
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adkikani
\((49^2 - 35^2)\) /14 =

A. 74
B. 76
C. 78
D. 79
E. 84
Show more


Ofcourse it is \(a^2-b^2=(a-b)(a+b)\)..
Here (49-35)(49+35)/14=14*84/14=84..

Do your calculations or observer the properties of number involved, of the calculations are difficult, and answer in a sec, ...

Both 49 and 35 have a 7 in them..
So we will get 7*7 in the product, one 7 from addition and other from subtraction..
One 7 gets cancelled out with 7 in 14..
Our ANSWER should be a MULTIPLE of 7..
Only E left
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(49^2 - 35^2)/14 = Updated on: 08 Feb 2021, 15:42
Originally posted by BrentGMATPrepNow on 10 Dec 2017, 20:56.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 15:42, edited 1 time in total.
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adkikani
\(\frac{(49^2 - 35^2)}{14} =\)

A. 74
B. 76
C. 78
D. 79
E. 84
Show more

(49² - 35²)/14 = (49 + 35)(49 - 35)/14
= (84)(14)/14
= 84
= E
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(49^2 - 35^2)/14 = 10 Dec 2017, 22:33
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adkikani
\(\frac{(49^2 - 35^2)}{14} =\)

A. 74
B. 76
C. 78
D. 79
E. 84
Show more
\(\frac{(49^2 - 35^2)}{14}=?\)

Start writing what you know, breaking numbers into pieces: \(49^2 = (49)(49)\), for example. And there are factors of 7 everywhere.

Factor everything, with cancellation in mind if you can, to reduce errors.

\(\frac{(49)(49) - (35)(35)}{(2*7)}=\)

\(\frac{(7*7*7*7) - (7*5*7*5)}{(2*7)}=\)

Notice two 7s in numerator's two terms, hence

\(\frac{49(7*7 - 5*5)}{(2*7)}=\)

\(\frac{49(49 - 25)}{(2*7)}=\frac{49*(24)}{2*7}=\)

\(\frac{(7*7)(2*12)}{2*7}= (7*12) = 84\)

Answer E
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(49^2 - 35^2)/14 = Updated on: 30 Nov 2023, 05:52
Originally posted by KarishmaB on 13 Dec 2017, 20:58.
Last edited by KarishmaB on 30 Nov 2023, 05:52, edited 1 time in total.
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adkikani
\(\frac{(49^2 - 35^2)}{14} =\)

A. 74
B. 76
C. 78
D. 79
E. 84
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Responding to a pm:
Quote:

Can this be also solved using unit digits?
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I am not sure what you mean. How do you intend to use unit's digit concept here?

You are probably confusing it with using units digit concept for remainders when dividing by 2, 5 or 10.
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(49^2 - 35^2)/14 = 27 Mar 2024, 08:05
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adkikani
\(\frac{(49^2 - 35^2)}{14} =\)

A. 74
B. 76
C. 78
D. 79
E. 84
Show more
\(\frac{­(49^2 - 35^2)}{14}\)

Or, \(\frac{­(49 - 35)(49 + 35)}{14}\)

Or, \(\frac{14*84}{14} = 84\), Answer will be (E)

 
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