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

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CEO
Joined: 21 Jan 2007
Posts: 2584
Location: New York City
If q, r and s are the numbers shown above, which of the foll  [#permalink]

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Updated on: 28 Jan 2014, 00:06
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:14) correct 33% (01:16) wrong based on 258 sessions

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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?

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.
Director
Joined: 26 Feb 2006
Posts: 846

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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
Senior Manager
Joined: 03 May 2007
Posts: 256

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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

CEO
Joined: 21 Jan 2007
Posts: 2584
Location: New York City

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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

yes, i thought plugging in 1.7 was a bit tedious, thoguht maybe there was a shorter way
Manager
Joined: 04 May 2007
Posts: 110

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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
SVP
Joined: 06 Sep 2013
Posts: 1694
Concentration: Finance
Re: q = 3 * r = 1 + 2 s = 3 + 14. If q, r and s are the  [#permalink]

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27 Jan 2014, 11:44
2
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
Intern
Joined: 22 May 2014
Posts: 26
Location: India
GMAT 1: 560 Q46 V29
GPA: 3.64
If q, r and s are the numbers shown above, which of the foll  [#permalink]

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Updated on: 14 Jun 2018, 09:01
1
$$q=3\sqrt{3}$$
$$r=1+2\sqrt{3}$$
$$s=3+\sqrt{3}$$

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.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2796
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
If q, r and s are the numbers shown above, which of the following show  [#permalink]

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14 Jun 2018, 05:25
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

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

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Intern
Joined: 16 Jul 2016
Posts: 39
Re: If q, r and s are the numbers shown above, which of the foll  [#permalink]

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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
Re: If q, r and s are the numbers shown above, which of the foll   [#permalink] 25 Jan 2019, 16:40
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