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

Question

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?

Himalayan · Answer

difficult question, but i choose: 

(B) q, s, r

Sergey_is_cool · Answer

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

bmwhype2 · Answer

yes, i thought plugging in 1.7 was a bit tedious, thoguht maybe there was a shorter way

gmatiscoming · Answer

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

jlgdr · Answer

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

GMATinsight · Answer

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

Henry S. Hudson Jr. · Answer

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

Sharky750 · Answer

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.

Insane09 · Answer

put √2=1.41 and √3=1.71
bingo you will solve the question in 30 sec
 answer=B

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

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

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