GRE Math Question (Set 1 of 4 Explained)

1. 7,532.418 The value of the The value of the number number in the in the Thousands place Thousandths place value value A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 7 Thousands , 5 Hundreds 3 Tens 2 Ones or Units .

4 Tenths 1 Hundredths 8 Thousandths 8>7

1

2. 7,532.418 The value of the number in the Hundreds place value

The value of the number in the Hundredths place value

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 7 Thousands , 5 Hundreds 3 Tens 2 Ones or Units .

4 Tenths 1 Hundredths 8 Thousandths 5>1

2

3. 7,532.418 The value of the The value of the number number in the Tens in the Tenths place value place value A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: 7 Thousands , 5 Hundreds 3 Tens 2 Ones or Units .

4 Tenths 1 Hundredths 8 Thousandths 3<4

3

4. 7,532.418 The amount of The amount of Units in Digits in the number the number above above A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: There are 3 digits to the left of the decimal and four digits to the right of the decimal. Thus, there are 7 digits.

The amount of the Units in the number above is just one. Units is a word that describes one place value. Please don’t misuse the term units.

Again, there is a maximum of one unit in any number.

If the question had asked for ‘The amount of the Units in the number above’, then the answer would be 2. 2 because that is the number in the Units place.

7>1

4

5.

2.3

2 + 3/10

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: There is a finite number of digits to the right of the decimal point. Thus, since each place value is a power of 10, every decimal can be converted to an integer divided by a power of 10. For example, 2.3 = 2 + 3/10 = 23/10

5

6.

90.17

90 + 17/100

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: If there are a finite number of digits to the right of the decimal point, converting a decimal to an equivalent fraction with integers in the numerator and denominator is a straightforward process. Since each place value is a power of 10, every decimal can be converted to an integer divided by a power of 10. For example, 90.17 = 90 + (17 / 100) = (9,000 + 17) / (100) = 9,017 / 100

6

7.

0.612

153/250

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: If there are a finite number of digits to the right of the decimal point, converting a decimal to an equivalent fraction with integers in the numerator and denominator is a straightforward process. Since each place value is a power of 10, every decimal can be converted to an integer divided by a power of 10. For example, 0.612 = 612 / 1000 Notice the right side, be precise, be attentive, and trust your preparation.

Preparation will teach you to make 1000 similar to 250.

612 / 4 = 153 1000 / 4 250

7

8.

The amount of place The amount of place values in the values in the decimal decimal form of 1/4 form of 52/25 A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: There are three place values of the decimal form of 1/4. 1/4 = 0.25.

0.25 has a value in the Ones (0), Tenths (2), and Hundredths (5) place values.

There are three place values of the decimal form of 52/25. 52/25 = 2.08.

2.08 has a value in the Ones (2), Tenths (0) , and Hundredths (8) place values.

The decimals that will either terminate, as in 1/4 = .25, never end and repeat a pattern, as in 1/9 = 0.0111111, or never end and not repeat a pattern, as in !2 = 1.41421356237

8

9.

The value of the The value of the number number in the in the Thousandths place Thousandths place value in the decimal value in the decimal form of 1/22 form of 1/9 A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: There are infinite place values of the decimal form of 1/9.

1/9 = 0.11111..... 0.11111.... has a value in the Ones (0), Tenths (1), Hundredths (1), Thousandths (1), Ten Thousandths (1) ..... place values.

There are three place values of the decimal form of 1/22.

1/22 = 0.0454545..... 0.0454545 has a value in the Ones (0), Tenths (0) , Hundredths (4), Thousandths (5), Ten Thousandths (4) ..... place values.

1< 5

9

10.

3/8

0.380

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: 1/8 = 0.125 3 (0.125) = .375 Rehearse, remember and re-use it on test day! Write the fractions ticker tape style and affix that to the bottom of your computer monitor.

1/19 = .0526315........

1/18 = 0.05555555.......

1/17 = 0.058823529.......

1/16 = 0.0625 1/15 = 0.066666666666666.....

1/14 = 0.071428577142857....

1/13 = 0.0769230769230....

1/12 = 0.083333333333.......

1/11 = 0.090909090909........

1/9 = 0.011 1/8 = 0.125 1/7 = 0.0142857142857142857....

1/6 = 0.1666666666666666666.....

10

11.

6.475

6 + 19/40

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: Use the denominator on the right to make the numbers similar.

6 (40) = 240 .4 (40) = 4 (4) = 16 .07 (40) = .7 (4) = 2.8 .005 (40) = 5 (.04) = .2 240 + 16 + 2.8 + .2 = 259 Thus, 6.475 = 259 / 40

11

12.

-0.30

-1/3

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 1/3 = 0.3333333......

-1/3 = -0.3333333.....

-0.30 > -0.333

12

13.

15/14

1.0741285

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: 15/14 = 1.07142857142857...... vs 1.0741285 1.071 < 1.074

13

14.

1.41420

!2

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: !2 = 1.41421356237......

1.41420 < 1.41421

14

15. 0.010110111011110111110.......

The increase in the number of ones in each successive group of ones

14/15

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 0.010110111011110111110. . . , has groups of consecutive 1â&#x20AC;&#x2122;s separated by a 0, where the number of 1â&#x20AC;&#x2122;s in each successive group increases by one.

14/15 = 0.93333333......

1 > 0.933333

15

16. Which answer correctly summarizes the place value of these digits using commas and periods?

7(1000) + 5(100) + 3(10) + 2(1) + 4 (1/10) + 1(1/100) + 8(1/1000) A. 7(10") + 5(10#) + 3(10$) + 2(10⁰) + 4(10$) + 1(10#) + 8(10") B. 7(10") + 5(10#) + 3(10$) + 2(10⁰) + 4(10⁻$) + 1(10⁻#) + 8(10⁻") C. 7,532,418.0 D. 8,142.357 E. None of the Above Correct: B Explanation: place value is the position of a number, defined by a power of ten.

7(1000) = 7 in the Thousands place 5(100) = 5 in the Hundreds place 3(10) = 3 in the Tens place 2(1) = 2 in the Ones place 4 (1/10) = 4 in the Tenths place 1(1/100) = 1 in the Hundredths place 8(1/1000) = 8 in the Thousandths place

16

17. Which answer has the INCORRECTLY underlined term

A. The decimal number system is based on representing numbers using powers of 10.

B. The place value of each digit corresponds to a power of 10.

C. Since each place value is a power of 10, every decimal can be converted to an integer divided by a power of 10.

D. Every fraction with integers in the numerator and denominator can be converted to an equivalent decimal by dividing the numerator by the denominator.

E. The decimal that results from any long division will either terminate, as in 1/4 = 0.25, or the decimal will have a repeating pattern without end, as in 1/22 = 0.045454545...

Correct: E Explanation: The decimal that results from any long division will either terminate, as in 1/4 = 0.25, or the decimal will have a repeating pattern without end, as in 1/22 = 0.045454545..., or the decimal will have a non-repeating pattern without end, as in !2 = 1.41421356237...

17

18. A true statement is worth 1 points. A false statement is worth only -1 point. Which answer correctly indicates the sum of the 5 independent statements below Statement 1. Every fraction with integers in the numerator and denominator is equivalent to a decimal that terminates or repeats.

Statement 2. every rational number can be expressed as either a terminating decimal as in 1/4 = .0.25, or as a repeating decimal, as in 25/12 = 2.08333333....

Statement 3. every terminating or repeating decimal represents a rational number.

Statement 4.Not all decimals are terminating or repeating; for instance, the decimal that is equivalent to !2 is 1.41421356237. . . , and it can be shown that this decimal does not terminate or repeat. Such numbers are called irrational numbers.

Statement 5. Every number with a finite number of digits to the right of the decimal point can be converted to an integer divided by a power of 10.

A. -5 B. -1 C. 3 D. 5 Correct: D Explanation: All are true

18

19.

15/14

Note* Do not consider any of the digits to the left of the decimal point while answering this question.

The value of the number in the decimal form of the fraction above that is the first to repeat

5

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 15/14 = 1.0714285714285714285714285.......

7>5

19

20.

1 x 10â °

0 x 10$

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 1 x 10â ° = 1 0 x 10$ = 0 1>0

20

21.

1 x 10#

10#

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: 1 x 10# = 100 10# = 100 Note, 0 x 10# = 0 100 > 100

21

22.

1 x 10â ť#

-1 x 10#

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: 1 x 10â ť# = 1/100 -1 x 10# = -100

1/100 > -100

22