Given that a = 7 -4sqrt3

Question

Given that

a=7-4\sqrt3 
 b=4\sqrt3-7 
 c=11-5\sqrt5 
 d=5\sqrt5-11 
 f=16 - 6\sqrt7

which of the above numbers is the smallest positive number?

A.  a 
B.  b 
C.  c 
D.  d 
E.  f

alamin8 · Answer

I am going to square each of the values
(a) 49 - 16x3 = 1
(b) 16x3 - 49 = -1 (out)
(c) 121 - 25x5 = -4
(d) 25x5 - 121 = 4
(f) 256 - 36x7 = 4

The least possible value is 1, and the answer is Option A.

kevincan · Answer

You got the right answer, but your reasoning isn’t sound

alamin8 · Answer

I 100% agree with you. I know that's not correct, but I have several ways to do the short-cut and tried to interchange the root, but it somehow gives me a huge answer.

Say, 7 - 4\sqrt{}3

In that case, we have to square the entire number, giving us, 49 - 56\sqrt{}3 + 48
or, 7 - 4x1.73 = 7 - 6.92 = 0.08 (approximately)

CrazyBlender123 · Answer

Not the conventional way to solve,
I knew that root(3)=1.732 
and 7-4(root(3)) is the closest to 0 i.e. 0.08

suntprovident · Answer

I solved the question using elimination and brute force

Looking at the question -

1. Smallest positive number required

Option b and c outright look suspicious where a bigger number is being subtracted from a smaller number.

* Quickly assuming √3 as 1.7 we can work out 4√3 as 5.5 and therefore negative - eliminate 
* Similarly √5 is greater than 2.2 so let's say around 2.23 and therefore negative - eliminate 
* Looking at the remaining options, E looks far fetched 
* Checking a and d gives us a closer

harjas2222 · Answer

according to the gmat club math book

The exponent rule allows us flexibility so we need to remember the exponent approx to (10)^1/2

a = 7 - 4(1.73)= 0.08
b= 4(1.73) - 7 = -0.08
c=11 -5(2.24) =-0.2
d=5(2.24) - 11=0.2
f=16 -6(2.65)
= 0.1

A) answer

kevincan · Answer

Also , 7 -4sqrt(3) = sqrt(49) - sqrt(48)

Given that a = 7 -4sqrt3

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Given that a = 7 -4sqrt3

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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