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If q, r and s are the numbers shown above, which of the foll

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bmwhype2
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If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   Updated on: 30 Nov 2022, 11:34
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\(q = 3\sqrt{3}\)

\(r = 1 + 2\sqrt{3}\)

\(s = 3 + \sqrt{3}\)

If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?

(A) q, r, s
(B) q, s, r
(C) r, q, s
(D) s, q, r
(E) s, r, q


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is there a shortcut to this question besides substituting 1.7 into each equation and working it out?
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B

Originally posted by bmwhype2 on 28 May 2007, 19:56.
Last edited by Bunuel on 30 Nov 2022, 11:34, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Himalayan
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   28 May 2007, 20:32
bmwhype2 wrote:
q = 3 * [3^(1/2)]
r = 1 + 2[3^(1/2)]
s = 3 + [3^(1/2)]

14. If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?
(A) q, r, s
(B) q, s, r
(C) r, q, s
(D) s, q, r
(E) s, r, q


is there a shortcut to this question besides substituting 1.7 into each equation and working it out?


difficult question, but i choose:

(B) q, s, r
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   28 May 2007, 20:38
if you substitute 3^(1/2) with 1.7 the problem is not that hard
q=5.1
r=4.4
s=4.7

q,s,r

answer is B
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   28 May 2007, 21:06
Sergey_is_cool wrote:
if you substitute 3^(1/2) with 1.7 the problem is not that hard
q=5.1
r=4.4
s=4.7

q,s,r

answer is B


yes, i thought plugging in 1.7 was a bit tedious, thoguht maybe there was a shorter way
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   28 May 2007, 21:56
nope, i think the only way to answer this question is to know that square root 3 is approx 1.7 and just multiply them all out
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   27 Jan 2014, 12:44
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bmwhype2 wrote:
q = 3 * [3^(1/2)]
r = 1 + 2[3^(1/2)]
s = 3 + [3^(1/2)]

14. If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?
(A) q, r, s
(B) q, s, r
(C) r, q, s
(D) s, q, r
(E) s, r, q


is there a shortcut to this question besides substituting 1.7 into each equation and working it out?


Haha, I don't know about tedious. Honestly, it only took me about 10 seconds to operate by 1.7 for all answer choices. I think that knowing that sqrt (3) = 1.7 and sqrt (2) = 1.4 approximately is a great shortcut in many problems. I think it is the fastest approach for this one

Just a quick reflection
Cheers!
J :)
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   14 Jun 2018, 06:25
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sarasjain20 wrote:
q=3\sqrt{3}
r=1+2\sqrt{3}
s=3+\sqrt{3}

14. If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?
(A) q, r, s
(B) q, s, r
(C) r, q, s
(D) s, q, r
(E) s, r, q


Please read the rules of posting

The best way forward in the question is the approximation

q=3\sqrt{3} = 3*1.7 = 5.1
r=1+2\sqrt{3} = 1+2*1.7 = 4.4
s=3+\sqrt{3} = 3+1.7 = 4.7

hence, q < s < r

Answer: Option B
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Henry S. Hudson Jr.
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   25 Jan 2019, 17:40
q=3root3
r=1+ 2root3
s=3+root3

Subtract root3 from each equation.

q=2root3
r=1+ 1root3
s=3

let's compare q and s by squaring each
q^2=12
s^2=9

so q>s

now let's compare r and s. Let's subtract root3 from both sides.

r=1+ 1root3
s=3

r=1root3
s=2

let's square each


r^2=3
s^2=4

s>r

so we have q>s>r
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   29 Oct 2020, 07:23
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bmwhype2 wrote:
\(q = 3\sqrt{3}\)
\(r = 1 + 2\sqrt{3}\)
\(s = 3 + \sqrt{3}\)

If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?

(A) q, r, s
(B) q, s, r
(C) r, q, s
(D) s, q, r
(E) s, r, q


is there a shortcut to this question besides substituting 1.7 into each equation and working it out?


Yes there is a shortcut or an alternate method.
\(q = 3\sqrt{3}\) write q as it is
\(r = 1 + 2\sqrt{3}\) . write this as \(1+\sqrt{3} +\sqrt{3}\)
\(s = 3 + \sqrt{3}\) write this as \( \sqrt{3}(\sqrt{3}+1)\)

so clearly observing the above trend we can see that
q is clearly the greatest.
and s>r since in this case multiplying \(\sqrt{3} \) to \(1+\sqrt{3}\) will yield a greater value than than adding .


hope this helps. Not exactly a shortcut but a method involving number sense.
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   24 Sep 2021, 23:41
put √2=1.41 and √3=1.71
bingo you will solve the question in 30 sec
answer=B
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink] If q, r and s are the numbers shown above, which of the foll   04 May 2023, 22:12
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Re: If q, r and s are the numbers shown above, which of the foll [#permalink]
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