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kamalakarthi
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Brent@GMATPrepNow
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√4If M = √4 + ∛4 + ∜4, then the value of M is:
A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4
√4 = 2
∛4
∛1 = 1
∛8 = 2
So, ∛4 is BETWEEN 1 and 2.
In other words, ∛4 = 1.something
∜4
∜1 = 1
∜16 = 2
So, ∜4 is BETWEEN 1 and 2.
In other words, ∜4 = 1.something
So, √4 + ∛4 + ∜4 = 2 + 1.something + 1.something
= more than 4
= E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Hi kamalakarthi,
As Brent has pointed out in his explanation, you don't really need to know the exact values of all 3 terms to answer the question. Notice how the answer choices are essentially "ranges" of answers? This is a clue that you don't necessarily need to calculate the exact answer. As you continue to study, be sure to pay attention to how the answer choices are written/formatted - they might provide a big clue as to how you can proceed through the prompt in the most efficient way possible.
GMAT assassins aren't born, they're made,
Rich
As Brent has pointed out in his explanation, you don't really need to know the exact values of all 3 terms to answer the question. Notice how the answer choices are essentially "ranges" of answers? This is a clue that you don't necessarily need to calculate the exact answer. As you continue to study, be sure to pay attention to how the answer choices are written/formatted - they might provide a big clue as to how you can proceed through the prompt in the most efficient way possible.
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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Just to add to Brent's solution:
√4 = 2
∜4 = √2 ≈ 1.4
(You can prove this as follows. ∜4 = 4^¼ = (2²)^¼ = 2^½ = √2.)
Since √4 > ∛4 > ∜4, we know that 2 > ∛4 > ≈1.4.
So √4 + ∛4 + ∜4 ≈ 2 + 1.6 + 1.4 ≈ 5. (This is remarkably close to the actual number, which is 5.0016...)
√4 = 2
∜4 = √2 ≈ 1.4
(You can prove this as follows. ∜4 = 4^¼ = (2²)^¼ = 2^½ = √2.)
Since √4 > ∛4 > ∜4, we know that 2 > ∛4 > ≈1.4.
So √4 + ∛4 + ∜4 ≈ 2 + 1.6 + 1.4 ≈ 5. (This is remarkably close to the actual number, which is 5.0016...)
