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# Which of the following are greater than 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 59181
Which of the following are greater than 1?  [#permalink]

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03 Jun 2019, 00:10
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:11) correct 42% (02:05) wrong based on 45 sessions

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Which of the following are greater than 1?

I. $$(\sqrt{82}-1.7^2) \div \sqrt{34}$$

II. $$\frac{9978.4 - 0.0083}{101^2}$$

III. $$\sqrt{143}\times 7^{1/3} \div 24.034$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

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Joined: 09 Mar 2018
Posts: 55
Location: India
Schools: CBS Deferred "24
Re: Which of the following are greater than 1?  [#permalink]

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03 Jun 2019, 00:56
IMO, the correct answer is A

One needs to be clear with common square values to answer under 2 mins.

1)$$(\sqrt{82}-1.7^2) / \sqrt{34}$$

now, we know 9 X 9 = 81 so, $$\sqrt{82}$$ will be slightly greater than 9

Further, 17 X 17 = 289 so, $$1.7^2 = 2.89$$

Without getting into decimals we can simply do ---> 9-3=6

Now, we know 6 X 6 = 36

So, $$\sqrt{34}$$ will be slightly less than 6

Finally, we can say $$\frac{6}{something less than 6}$$ will always be > 1

Hence, 1 is true.

2. $$\frac{9978.4−0.0083}{101^2}$$

100 X 100 = 10000

Now, since 0.0083 is so small we can simply ignore it and the fraction will remain to be

$$\frac{9978.4}{10000}$$

It is clear that value will be something 0.99xxxx

so, definitely less than 1

3.$$\sqrt{143} X 7^{1/3} / 24.034$$
Now, 12 X 12 = 144, so the value $$\sqrt{143}$$ of will be slightly less than 12

2^3 =8, so the value of $$7^{1/3}$$ will be slightly less than 2

Now, even if we take 11.99 X 1.99 it will always be less than the denominator i.e 24.034

Hence, it is less than 1
Re: Which of the following are greater than 1?   [#permalink] 03 Jun 2019, 00:56
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# Which of the following are greater than 1?

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