If r=0.345, s=(0.345)^2, and t=root(0.345), which of the

Hi All,

This prompt showcases some great Number Property rules that you're likely to face (in some way or another) on the Official GMAT.

Regardless of the actual numbers involved, IF you're dealing with a positive fraction (meaning a value that is greater than 0 and less than 1), then there are some rules to remember...

1) Squaring that fraction will make the result SMALLER
2) Square-rooting that fraction will make the result BIGGER

Here are some additional Number Property rules for NEGATIVE fractions (meaning a value that is less than 0 and greater than -1)....

1) Squaring that fraction will make the result BIGGER (since squaring a negative creates a positive) AND the result will be CLOSER to 0.
2) Cubing that fraction will make the result BIGGER (since the result will be closer to 0).

GMAT assassins aren't born, they're made,
Rich

If \(r=0.345\), \(s=0.345^2\), and \(t=\sqrt{0.345}\), which of the following is the correct ordering of \(r\), \(s\), and \(t\) ?

A. r < s < t
B. r < t < s
C. s < t < r
D. s < r < t
E. t < r < s

If \(x\) is in the range \(0<x<1\) then: \(0<x^2<x<\sqrt{x}<1\).

Consider the simpler example: if \(x=\frac{1}{4}\) then \(0<\frac{1}{16}<\frac{1}{4}<\frac{1}{2}<1\).

So, \(s<r<t\).

Answer: D.
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CONCEPT:For solving any such question, One must know that

1) If 0<x<1, then the higher powers of x result in smaller numbers and lower powers of x result in a bigger number
2) If x>1, then the higher powers of x result in Bigger numbers and lower powers of x result in a Smaller number



Here since 0.345 is between 0 and 1 therefore

the number with the highest power i.e. s must be least
and the number with the Lowest power i.e. t must be Biggest number

therefore s < r < t

Answer: Option

Hi All,

This question is based on a couple of important Number Property rules regarding positive fractions (between 0 and 1):

1) When 'squaring' a positive fraction, the result gets SMALLER (e.g.. (1/2)^2 = 1/4).

Since 'square-rooting' is the opposite of 'squaring'....

2) When 'square-rooting' a positive fraction, the result gets BIGGER.

While these rules are not tested that often on the Official GMAT, it's likely that you'll be tested on either or both at least once on Test Day.

GMAT assassins aren't born, they're made,
Rich

Let \(r = 0.36\) ; \(s = 0.36^2\) & \(t = \sqrt{0.36}\)

So, \(r = 0.36 , s ≈ 0.13\) & \(t = 0.60\)

Thus, \(s < r < t = 0.13 < 0.36 < 0.60\)

Hence, answer will be (D) \(s < r < t\)
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Since r is a positive decimal between 0 and 1, s = r^2 and t = √r. We see that when r is raised to a power > 1, its value decreases, and when it is raised to a power < 1, its value increases (recall that square root means ½ power). Thus, the correct ordering is s < r < t.

Answer: D
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Solution

Given:

• r=0.345
• s=\(0.345^2\)
• t=√0.345

To find:

• The correct order of r, s, and t among the given options.

Approach and Working

For 0< x <1:

• On increasing the power of x, the value of power of x will decrease.

o For example: 0.5 >\(0.5^2\)

• On decreasing the power of x, the value of power of x will increase.

o For example: \(0.5^2\) < 0.5

Thus, we can conclude that: s< r and r <t
• Hence, s < <r < t

Correct answer: Option D
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If r=0.345, s=0.3452, and t=√0.345, which of the following is the correct ordering of r, s, and t ?

A. r < s < t
B. r < t < s
C. s < t < r
D. s < r < t
E. t < r < s

Tricky part of this question is getting rid of that pesky square root for t. Square everything

r=0.345, s=0.3452, and t=√0.345
r^2=0.345^2, s^2=0.3452^2, and t^2=0.345

t > r > s

D.
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