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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] New post  Updated on: 28 Jan 2014, 00:06
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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


is there a shortcut to this question besides substituting 1.7 into each equation and working it out?
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Originally posted by bmwhype2 on 28 May 2007, 18:56.
Last edited by Bunuel on 28 Jan 2014, 00:06, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Himalayan
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Re: PS #14 radicals [#permalink] New post  28 May 2007, 19:32
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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Sergey_is_cool
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[#permalink] New post  28 May 2007, 19:38
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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bmwhype2
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[#permalink] New post  28 May 2007, 20:06
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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gmatiscoming
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[#permalink] New post  28 May 2007, 20:56
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: q = 3 * r = 1 + 2 s = 3 + 14. If q, r and s are the [#permalink] New post  27 Jan 2014, 11:44
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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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If q, r and s are the numbers shown above, which of the foll [#permalink] New post  Updated on: 14 Jun 2018, 09:01
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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) \(s, r, q\)

Originally posted by sarasjain20 on 14 Jun 2018, 05:01.
Last edited by generis on 14 Jun 2018, 09:01, edited 2 times in total.
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If q, r and s are the numbers shown above, which of the following show [#permalink] New post  14 Jun 2018, 05:25
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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] New post  25 Jan 2019, 16:40
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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Sharky750
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If q, r and s are the numbers shown above, which of the foll [#permalink] New post  29 Oct 2020, 06:23
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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