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# (58^2 + 58^2)/29^2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 64240

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30 Dec 2014, 06:46
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:07) correct 24% (01:32) wrong based on 130 sessions

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Tough and Tricky questions: Arithmetic.

(58^2 + 58^2)/29^2 =

A. 4
B. 8
C. 29
D. 58
E. 116

Kudos for a correct solution.

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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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30 Dec 2014, 07:14
The question looks quite terrifying when you just look at the question stem, but once you check the answer alternatives, it is actually quite fun. With a little bit of simplification, you can make a strategic guess, since the alternatives are quite far apart.

First, let's simplify the expression a bit:

$$\frac{(58^2+58^2)}{28^2}=\frac{2*58^2}{28^2}=\frac{2*2^2*29^2}{2^2*2^2*7^2}=\frac{29^2}{2*7^2}$$.

We can't simplify the equation further, so now we can start guessing. 29 is close to 30, so the numerator should be just short of $$30^2=900$$. The denominator is 2 times 49, so just below 100. 900 over 100 is 9, so the result should be just short of that. Checking the answer choices, we see that B is 8, so that must be the answer.

If you are still not convinced, you can compare the numberator with $$25^2=625$$. 625 over 100 would be 6.25 and since 29 is closer to 30 than to 25, the precise result should be somewhere between 6.25 and 9, however closer to 9 than to 6.25.
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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30 Dec 2014, 14:50
My solution is the following. 58 is approximately equal to 60 and 28 is app. equal to 30. So we have the following fraction: ((60^2)+(60)^2)/(30^2)=(2*3600)/900=(7200/900)=8 Answer B (The exact figure is 8.5)
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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30 Dec 2014, 18:11

$$\frac{(58^2 + 58^2)}{28^2} = \frac{2 * 58^2}{28^2}$$

$$= \frac{2 * (60-2)^2}{(30-2)^2}$$

$$= \frac{2 (60^2 - 2*60*2 + 4)}{30^2 - 2*30*2 + 4}$$

$$= \frac{2 * 60^2}{30^2}$$

$$= 2 * 2^2 = 8$$
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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30 Dec 2014, 21:40
By approximation, 58/28 = ~2 (lower side)
2^2 + 2^2 = 8
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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31 Dec 2014, 02:48
There was a typo. Question reads: (58^2 + 58^2)/29^2 =

Edited.
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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31 Dec 2014, 02:55
Wow. With that corrected type this becomes really easy, as we don't need to make any approximations:

$$\frac{2*(58^2*58^2)}{29^2}=\frac{2*2*2*29^2}{29^2}=8$$
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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31 Dec 2014, 03:06
1
= {(29 x 2)^2 + (29x2)^2}/29^2
= {(29^2) X (2^2)/(29^2)} +{(29^2) X (2^2)/(29^2)}
= 2^2+2^2
= 8
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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31 Dec 2014, 08:05
Bunuel wrote:

Tough and Tricky questions: Arithmetic.

(58^2 + 58^2)/29^2 =

A. 4
B. 8
C. 29
D. 58
E. 116

Kudos for a correct solution.

(58^2 + 58^2)/29^2 = 2 (58^2)/29^2 = 2 * (2^2 * 29^2) / 29^2 = 2 * (2^2) = 2 * 4 = 8

Ans 8
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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31 Dec 2014, 12:50
1
Ans is 8
my approach was:
(58^2 + 58^2)/29^2 =58(58+58)/29*29
=58*116/29*29=2*4=8
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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02 Jan 2015, 06:38
1
(58^2 + 58^2)/29^2
--> 2 * (58^2) / 29^2
--> 2 * ((29 * 2)^2) / 29^2
--> (2^3) * (29^2) / 29^2
--> 2^3 = 8
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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02 Jan 2015, 06:48
1
$$29^2(2^2+2^2)/29^2$$
simplify by $$29^2$$

we get $$2^2+2^2=8$$
answ. B
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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03 Jan 2015, 01:41
the given (58^2+58^2)/29^2= 2*58^2/29^2 == 2*29^2*2^2/29^2 = 2*2*2= 8
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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08 Jan 2015, 08:38
Bunuel wrote:

Tough and Tricky questions: Arithmetic.

(58^2 + 58^2)/29^2 =

A. 4
B. 8
C. 29
D. 58
E. 116

Kudos for a correct solution.

OFFICIAL SOLUTION:

(B) There are many ways to solve this problem. The easiest is probably to factor the numerator and then cancel terms.
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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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11 Aug 2019, 21:34
29^2 * (2^2 + 2^2)/29^2=
4+4=8
Option B

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Re: (58^2 + 58^2)/29^2 =  [#permalink]

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11 Aug 2019, 22:29
Bunuel wrote:

Tough and Tricky questions: Arithmetic.

(58^2 + 58^2)/29^2 =

A. 4
B. 8
C. 29
D. 58
E. 116

Kudos for a correct solution.

29^2(4+4)/29^2= 8

IMO B

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Re: (58^2 + 58^2)/29^2 =   [#permalink] 11 Aug 2019, 22:29