Which of the following is the closest approximation to

Question

Which of the following is the closest approximation to    ÷   ?

A. 10
B. 15
C. 20
D. 25
E. 30

Archit3110 · Answer

÷  
8*15/(2+4) = 20
IMO C

cantaffordname · Answer

Here we have can see that √ of 73 is close to 81 rather than 64 so the closest value for it would be 9. Similarly √ of 239 is closest to the value of √ of 225, i.e 15.

Hence 9*15/2+4 = 19.28 which is closest to 20. So IMO : it's C

ScottTargetTestPrep · Answer

√73 is about 8.5.

√239 is about 15.5.

√7.2 is about 3.

√15.7 is about 4.

15.5 x 8.5 = 131.75 or about 130

3 + 4 = 7

Thus,

130/7 is about 20.

Answer: C

TheNightKing · Answer

I calculated the lowest and highest possible values of the expressions. 
Lowest means (8*15)/(2+3) and highest means (9*16)/(3+4). The results are 24 and 20.XX. So the closest approximation is 20.

P.S: 25 cannot be the answer as the max value is 24 so C it is

Nipungupta9081 · Answer

IMO C

73 taken as 72 ( square root )= 8
239 taken as 225 = 15

7.2 taken as 4 = 2 
15.7 taken as 16 = 4

= 8*15 / 2 + 4
= 8 * 15 / 6
= 20

sujoykrdatta · Answer

We have: √73 ∗ √239 ≈ √81 ∗ √225 = 9 ∗ 15 = 135
 Note that 73 was increased to 81 and 239 decreased to 225, this kind of compensates each other

Again: √7.2 + √15.7 ≈ √8 + √16 = 2√2 + 4 = 2 ∗ 1.4 + 4 = 6.8 ≈ 7

Thus:    ÷    
= 135 ÷ 7
= 19.3

Closest option is Option C

dp1234 · Answer

Approximate to all to next higher squares - 73 to 81, 239 to 256, 7.2 to 9 and 15.7 to 16. 
Thus we would get (9 x 16) /(3 +4) = 144/7 = 20.5 
Ans is  C

nemoexplicabo · Answer

This is a fantastic problem for practicing estimation and approximation — skills that are absolutely critical for saving time on the GMAT, especially on questions involving square roots.

The secret here is to approximate each square root to nearby perfect squares, then simplify the expression. Let me show you how:

Step 1: Approximate the square roots in the numerator

√73 ≈ √64 = 8 or √81 = 9 → √73 is between 8 and 9, closer to 8.5
√239 ≈ √225 = 15 or √256 = 16 → √239 is between 15 and 16, closer to 15.5

For cleaner mental math, I'll use √73 ≈ 8.5 and √239 ≈ 15.5

Numerator ≈ 8.5 × 15.5

To multiply these quickly:
8.5 × 15.5 = 8.5 × 15 + 8.5 × 0.5
= 127.5 + 4.25
≈ 131.75

Or think of it as: (8.5)(15.5) ≈ (9)(16) = 144 (slight overestimate)
So the numerator is around 130-135.

Step 2: Approximate the square roots in the denominator

√7.2 ≈ √9 = 3, but 7.2 is closer to √4 = 2 → Actually, √7.2 ≈ 2.7
√15.7 ≈ √16 = 4

Denominator ≈ 2.7 + 4 = 6.7

Step 3: Divide

Final calculation ≈ 132 ÷ 6.7 ≈ 132 ÷ 7 ≈ 19-20

Looking at the answer choices, 20 is the closest.

Answer: C

Common traps to avoid:

A big mistake is trying to calculate the exact values — that will eat up way too much time and isn't necessary on approximation questions. Another pitfall is approximating too roughly. For instance, if you approximate √73 as 8 and √239 as 15, you get 120 in the numerator, which might lead you to answer B (15) instead of C (20). The key is finding the balance between speed and accuracy.

Key takeaway: Approximation questions reward smart rounding, not perfect precision. When you see square roots with non-perfect squares, immediately think about the nearest perfect squares above and below. Practice estimating products and quotients mentally — it's a skill that will save you minutes on test day!

Lokesh3 · Answer

Let's say ans is x
√73 ~ √(9*8), √239 =√(8*10*3) which is greater than √(8*9*3)
x>√(9*8*9*8*3)/(2.7+4)
x>9*8*√3/6.7
x>9*8*1.7/6.7
x>9*8/4
x>18
Closest to 18 and greater than 18 is 20

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=jGXOFYA68PY

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