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555-605 (Medium)|   Algebra|      
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Bunuel
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If 60/x + 288/x^2 = 7, which of the following could be the value of x? 16 Mar 2020, 08:27
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82% (01:56) correct 18% (02:26) wrong based on 383 sessions

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If \(\frac{60}{x} + \frac{288}{x^2} = 7\), which of the following could be the value of x?

(A) 6
(B) 8
(C) 9
(D) 12
(E) 15
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D
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Kinshook
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If 60/x + 288/x^2 = 7, which of the following could be the value of x? 16 Mar 2020, 09:21
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Bunuel
If \(\frac{60}{x} + \frac{288}{x^2} = 7\), which of the following could be the value of x?

(A) 6
(B) 8
(C) 9
(D) 12
(E) 15
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Asked: If \(\frac{60}{x} + \frac{288}{x^2} = 7\), which of the following could be the value of x?

\(60x + 288 = 7x^2\)
\(7x^2 - 60x - 288 = 0\)

x = (60 +- 108)/14
x = 12 or -24/7

IMO D
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If 60/x + 288/x^2 = 7, which of the following could be the value of x? 16 Mar 2020, 13:01
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Bunuel
If \(\frac{60}{x} + \frac{288}{x^2} = 7\), which of the following could be the value of x?

(A) 6
(B) 8
(C) 9
(D) 12
(E) 15
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We can easily form a quadratic equation and solve it.

However, we can use the options as well:

We have: 60/x + 288/x^2 = 7

Option A: x = 6: 60/x itself is 10; so the sum of the 2 terms above cannot be 7
Option B: x = 8: 60/x itself is greater than 7; so the sum of the 2 terms above cannot be 7
Option C: x = 9: 60/9 is greater than 6 and 288/81 is greater than 3; so the sum of the 2 terms above cannot be 7
Option D: x = 12: 60/x is 5 and 288/144 is 2; so the sum of the 2 terms is 7 ---- correct

Just for the sake of observation:
Option E: x = 15: 60/15 is 4 and 288/225 is less than 2; so the sum of the 2 terms above cannot be 7

Answer D
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Edwinnguyen
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If 60/x + 288/x^2 = 7, which of the following could be the value of x? 16 Mar 2020, 21:23
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I think with this question we should not solve the equation - let's try to test 5 choices

A - 60/6 = 10 > 7 - E
B & C: 60/x has the remainer - E
D: Got it - reconfirm after test with number
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If 60/x + 288/x^2 = 7, which of the following could be the value of x? 06 Aug 2024, 02:33
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It might be more complicated than necessary but I notice that 288 can be written as 2*144 and that 144 is simply 12^2. I also noticed that 60 can be rewritten as 5*12. Therefore I rewrote the equation as:

5(12/x) + 2(12/x)^2 = 7.

I substituted 12/x as y yielding

5y + 2y^2 - 7 = 0.

The roots for this equation are y = 1 or -7/2. A quick glance down the answer choices and keeping in mind that y = 12\x made me realise the answer would have been 12.
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Tarunw111
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If 60/x + 288/x^2 = 7, which of the following could be the value of x? 29 Sep 2025, 00:58
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putting the options
We can put multiples of 6 for x so that it comes as a whole number.
Try putting 6 and 12.
for 12, the values comes 7.
Thanks!
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