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The sum of two numbers is 100 and their difference is 37. The differen

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Bunuel
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The sum of two numbers is 100 and their difference is 37. The differen [#permalink] New post   09 May 2022, 02:45
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The sum of two numbers is 100 and their difference is 37. The difference of their squares is:

(A) 37
(B) 63
(C) 100
(D) 3700
(E) 4700
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D
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thkkrpratik
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Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink] New post   09 May 2022, 03:01
Bunuel wrote:
The sum of two numbers is 100 and their difference is 37. The difference of their squares is:

(A) 37
(B) 63
(C) 100
(D) 3700
(E) 4700


Given:
\(x + y = 100\)
\(x - y = 37\)

To find:
\(x^2 - y^2 = ?\)

From the given info, add both:
\(2x = 137\)
\(x = \frac{137}{2}\)
\(Then, y = \frac{63}{2}\)

\(x^2 - y^2 =\frac{137^2}{2^2} - \frac{63^2}{2^2}\)
= \(\frac{1}{4} (137^2 - 63^2)\)
= \(\frac{1}{4} (137 + 63)(137 - 63)\)
= \(\frac{1}{4} (200)(74)\)
= 50 x 74
= 3700

Option D
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Nefertiti9
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The sum of two numbers is 100 and their difference is 37. The differen [#permalink] New post   09 May 2022, 03:23
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IMO D
a+b=100
and
a-b=37
we know,
\((a+b)(a-b)=a^2-b^2\)
=>\(a^2-b^2= 37*100=3700\)
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thkkrpratik
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Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink] New post   09 May 2022, 04:31
Nefertiti9 wrote:
IMO D
a+b=100
and
a-b=37
we know,
\((a+b)(a-b)=a^2-b^2\)
=>\(a^2-b^2= 37*100=3700\)


Easier and time saving!
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Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink] New post   09 May 2022, 10:31
Bunuel wrote:
The sum of two numbers is 100 and their difference is 37. The difference of their squares is:

(A) 37
(B) 63
(C) 100
(D) 3700
(E) 4700

\(a + b = 100\) ; \(a - b = 37\)

We know, \(a^2 - b^2 = (a + b)(a - b)\)

Thus, \(a^2 - b^2 = 100*37 => 3700\), Answer will be (D)
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Re: The sum of two numbers is 100 and their difference is 37. The differen [#permalink]
09 May 2022, 10:31
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