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GRE MINI-Tests - Quant & Verbal #4 : General GRE Questions & Strategies

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
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Mini-test #4 QQ #3 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Given that O is the center of the circle

Attachment:
GRE circle (15).jpg
GRE circle (15).jpg [ 11.86 KiB | Viewed 2638 times ]


Now, OA = OB = Radius of the circle, r (Assume)
In △AOB, ∠AOB ~ 90°

=> We can apply Pythagorean theorem in △AOB
=> AB^2 = \(OA^2\) + \(OB^2\) = \(r^2\) + \(r^2\) = 2*\(r^2\)
=> AB = r*\(\sqrt{2}\)

Clearly, Quantity B (AB) > Quantity A (OA)

So, Answer will be B
Hope it helps!

Watch the following video to Learn Basics of Circles

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
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Mini-test #4 QQ #4 Solution

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Given that x is a positive integer and k is the remainder when \(x^3-x\) is divided by 3.

\(x^3-x\) = x*(\(x^2-1\)) = (x-1)*x*(x+1) = Product of three consecutive integers
=> \(x^3-x\) will be divisible by 3! => will be divisible by 3
=> Remainder of \(x^3-x\) by 3 = 0 => k = 0

Clearly, Quantity B (1) > Quantity A (k=0)

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
Mini-test #4 QQ #5 Solution

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Ben is three times as old as Ron
B = 3*R = 3R

Ed is 8 years younger than Ben
E = B - 8 = 3R - 8

Ron is 7 years older than Ken
=> R = K + 7
=> K = R - 7

Sum of the ages of all four people is 161
=> R + B + E + K = 161
=> R + 3R + 3R - 8 + R - 7 = 161
=> 8R = 161 + 15 = 176
=> R = \(\frac{176}{8}\) = 22

So, Answer will be C
Hope it helps!
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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
Mini-test #4 QQ #6 Solution

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We need to arrange \(2 \sqrt{13}, 4 \sqrt{3}, 5 \sqrt{2}, and 3 \sqrt{6}\) in ascending order

\(2 \sqrt{13}, 4 \sqrt{3}, 5 \sqrt{2}, and 3 \sqrt{6}\) are square roots multiplied by positive integer
=> all are positive

So, comparing these terms is same as comparing square of these terms

=> \((2 \sqrt{13})^2, (4 \sqrt{3})^2, (5 \sqrt{2})^2, and (3 \sqrt{6})^2\)
=> 4*13, 16*3, 25*2, 9*6
=> 52, 48, 50, 54

=> \(4 \sqrt{3} < 5 \sqrt{2}<2 \sqrt{13}<3 \sqrt{6}\)

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Roots

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
Mini-test #4 QQ #7 Solution

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Given that f(x)=x^2+4, and f(2k)=36 and we need to find the value of k

f(x)=x^2+4
=> f(2k)=(2k)^2+4 = 4k^2 + 4 = 36(given)
=> 4k^2 = 32
=> k^2 = 8
=> k = +2\(\sqrt{2}\) or -2\(\sqrt{2}\)

So, Answer will be D
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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
Mini-test #4 QQ #8 Solution

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In a population of chickens, the average (arithmetic mean) weight is 6.3 pounds, and the standard deviation is 1.2 pounds.

Mean, M = 6.3
Standard Deviation, SD = 1.2

Which of the following weights (in pounds) are within 1.5 units of the standard deviation of the mean?

We need to find the values which are M - 1.5*SD and M + 1.5*SD
=> Value between 6.3 - 1.5*1.2 and 6.3 + 1.5*1.2 = 4.5 and 8.1

So, Answer will be B, C, D, E, F, G
Hope it helps!

Watch the following video to Learn the Basics of Statistics

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
Mini-test #4 QQ #9 Solution

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In the standard x,y plane, what is the slope of the line that is perpendicular to the line 12x + 3y - 7=0

Slope of line (m) 12x + 3y - 7=0 is given by -(Coefficient of x)/(Coefficient of y) = \(\frac{-12}{3}\) = -4

Let slope of the perpendicular line be \(m_1\)

Since the lines are perpendicular => m * \(m_1\) = -1
=> -4 * \(m_1\) = -1
=> \(m_1\) = \(\frac{1}{4}\)

So, Answer will be \(\frac{1}{4}\)
Hope it helps!

Watch the following video to learn the Basics of Slope of a Line

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
Mini-test #4 QQ #10 Solution

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Given below Box and Whisker Plot with 5 number summary as

Minimum = 0
First Quartile = 9
Median = 25
Third Quartile = 56
Maximum = 139

Attachment:
GRe wiskey plot.jpg
GRe wiskey plot.jpg [ 75.61 KiB | Viewed 2659 times ]


Interquartile Range (IQR) = Third Quartile - First Quartile = 56 - 9 = 47

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Box and Whisker Plot

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Re: GRE MINI-Tests - Quant & Verbal #4 [#permalink]
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