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555-605 (Medium)|   Algebra|   Arithmetic|      
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taha1234
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= Updated on: 08 Jul 2021, 06:47
Originally posted by taha1234 on 08 Jul 2021, 05:22.
Last edited by taha1234 on 08 Jul 2021, 06:47, edited 1 time in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

77% (02:12) correct 23% (02:10) wrong based on 261 sessions

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Not Attempted Yet
\(\frac{1527^2 - 1473^2}{(67)(54)+(54)(58)}=\)

A.12
B. 24
C. 30
D. 36
E. 42
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B
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 08 Jul 2021, 06:42
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Dear taha1234 ,

The answer is not matching with options. please check the Question.
Answer coming for this question 333.3 .

Bunuel pls check question.

Regards,
Rajat
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taha1234
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 08 Jul 2021, 06:51
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Yes, there was a mistake.
Thank you rajatchopra1994 for pointing it out.
I have edited the question; now it is correct.
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 08 Jul 2021, 06:56
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Explanation:

= [(1527+1473)*(1527-1473)] / [54*(67+58)]
= (3000*54)/(125*54)
= 3000/125
= 24

IMO-B

Posted from my mobile device
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 13 Jul 2021, 14:07
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confused as to how this solution was reached. Can you shed some light?
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 13 Jul 2021, 15:06
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Hello!

Here is another tricky question trying to lure you in to do tons of math. But we are not going to let them. We are going to be sneaky and find the trick.

The first clue should be the number 54, which is repeated twice in the denominator. Pull it out to simplify the expression

\(\frac{\\
1527^{2} - 1473^{2}}{54(67+58)}\)

That's nice, but the numerator still gives me nightmares. Is it likely that the number 54 figures there as well?

Good thinking, but before you start dividing large numbers by 54, what else do you notice about the numerator?

It is a quadratic expression of the form \( x^{2} - y^{2} = (x+ y)(x - y)\)

You have to learn these standard quadratic expressions, the Special Products, as they are lifesavers on questions like these

\(1527^{2} - 1473^{2}\) is therefore equal to (1527 + 1473)(1527 - 1473)

Here unfortunately (or fortunately if you love math like I do) you have to do some math

1527 + 1473 = 3000

1527 - 1473 = 54

The numerator is therefore equal to 54(3000)

What do you know, 54 again

The whole fraction now looks like this:

\(\frac{54(3000)}{54(67+58)}\)

Cancel out the 54 from the numerator and the denominator

67 + 58 = 125

\(\\
\frac{3000}{125 }\) = 24

The answer is (B)
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 13 Jul 2021, 21:18
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Ok3r4
confused as to how this solution was reached. Can you shed some light?
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Dear Ok3r4 ,

As we know, a^2 - b^2 is (a+b)(a-b)
I have used this formula. Take common out of the equation and solve it.

Regards,
Rajat
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 13 Jul 2021, 23:50
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\(a^2 - b^2 = (a - b) (a + b) \)

Numerator: \((1527)^2 - (1473)^2 = (1527 - 1473) (1527 + 1473) = 54 * 3000\)

Denominator: Take 54 common and then we have 54 (67 + 58)

=> \(\frac{(54 * 3000) }{ 54 * 125}\)

=> \(\frac{3000}{125} = 24\)

Answer B
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15272−14732(67)(54)−(54)(58)=15272−14732(67)(54)−(54)(58)= 18 Jul 2023, 07:30
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