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20 Minutes Test: Number Systems 1 - GMAT MCQ


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10 Questions MCQ Test Quantitative for GMAT - 20 Minutes Test: Number Systems 1

20 Minutes Test: Number Systems 1 for GMAT 2025 is part of Quantitative for GMAT preparation. The 20 Minutes Test: Number Systems 1 questions and answers have been prepared according to the GMAT exam syllabus.The 20 Minutes Test: Number Systems 1 MCQs are made for GMAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for 20 Minutes Test: Number Systems 1 below.
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20 Minutes Test: Number Systems 1 - Question 1

The value of  is 

Detailed Solution for 20 Minutes Test: Number Systems 1 - Question 1

Factoring √12 and √27 and solving, we get
√12 = √(4 x 3) = √(2 x 2 x 3) = 2√3
√27 = √(9 x 3) = √(3 x 3 x 3) = 3√3

Now the equation we get is 3√12 / 6√27. On substituting the values from above, we get

20 Minutes Test: Number Systems 1 - Question 2

If 3x + 64 = 26 + (√3)8, then the value of ‘x’ is 

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20 Minutes Test: Number Systems 1 - Question 3

The number (3 − √3)(3 + √3) is:

Detailed Solution for 20 Minutes Test: Number Systems 1 - Question 3

The given expression is in the form of (a - b)(a + b), which is a standard identity:

(a - b)(a + b) = a² - b²

Here,
a = 3
b = √3

Now apply the identity:

(3 - √3)(3 + √3) = 3² - (√3)² = 9 - 3 = 6

So, the result is 6, which is a rational number.

20 Minutes Test: Number Systems 1 - Question 4

Express 0.375 as a fraction in its simplest form.

Detailed Solution for 20 Minutes Test: Number Systems 1 - Question 4

To convert 0.375 into a fraction, write it as 375/1000. Simplify by dividing both numerator and denominator by 125, which gives 3/8.

20 Minutes Test: Number Systems 1 - Question 5

On simplifying (√5 + √7)², we get

Detailed Solution for 20 Minutes Test: Number Systems 1 - Question 5

We use the identity
(a + b)² = a² + 2ab + b²

Here,
a = √5
b = √7

Now apply the identity:

(√5 + √7)² = (√5)² + 2 × √5 × √7 + (√7)²
= 5 + 2√35 + 7
= 12 + 2√35

20 Minutes Test: Number Systems 1 - Question 6

The value of  is 

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20 Minutes Test: Number Systems 1 - Question 7

The value of (0.00032)-2/5 is

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20 Minutes Test: Number Systems 1 - Question 8

Ifn x = 3+2√2, then the value of 

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20 Minutes Test: Number Systems 1 - Question 9

8√15 ÷ 2√3

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20 Minutes Test: Number Systems 1 - Question 10

√8+2√32−5√2 is equal to

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