Understanding decimals - GMAT Quantitative

Given that

it follows that .

We don't need to know or , the only important information is that:

Where the remainder is any one of the answer choices. This is because the remainder for any divisor/dividend pair is the product of the decimal portion of the quotient and the divisor.

Since we don't know y, our answer choice for the remainder is any answer that satisfies the above equation for a positive interger, since is specified as such in the problem.

The only answer choice that satisfies the constraints on is 184:

==> ==>

One hundred seven ten-thousandths = 0.0107

Seventeeen one-hundredths = 0.17, or 0.1700

The sum:

This is one thousand eight hundred seven ten-thousandths.

Seventy-seven one-hundredths = 0.77

Sixty-six one-thousandths = 0.066

The product:

0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right.

This is five thousand eighty-two hundred-thousandths.

Eight hundred eighty-eight thousandths = 0.888

Sixty-four ten-thousandths = 0.0064

Set up a long division:

Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.

(Note that leading zeroes have been removed.)

Carry out the long division, making sure you align the decimals:

The quotient of this division is that of the original problem, so the correct choice is 138.75.

Twenty-seven one-thousandths = 0.027

Its square is

Multiply without regard to the decimals first:

0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

This is seven hundred twenty-nine one-millionths.

Fifteen one-hundredths = 0.15

Its cube is

Multiply without regard to the decimals first:

0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

This is three thousand three hundred seventy-five one-millionths.

Although tempting, a calculator is not required to spot the correct answer.

is equal to as it is parts of . And therefore must be slightly different. (It's it actually )

The tenth digit after the decimal point is 3.

When dividing 1 by 3 or 10 by 3, we get repeating 3s. So, there must be a 3 in the tenths digit.

Given that

it follows that .

We don't need to know or , the only important information is that:

Where the remainder is any one of the answer choices. This is because the remainder for any divisor/dividend pair is the product of the decimal portion of the quotient and the divisor.

Since we don't know y, our answer choice for the remainder is any answer that satisfies the above equation for a positive interger, since is specified as such in the problem.

The only answer choice that satisfies the constraints on is 184:

==> ==>

One hundred seven ten-thousandths = 0.0107

Seventeeen one-hundredths = 0.17, or 0.1700

The sum:

This is one thousand eight hundred seven ten-thousandths.

Nine hundred six ten-thousandths = 0.0906

Four tenths = 0.4, or 0.4000

The difference:

This is three thousand ninety-four ten-thousandths.

Seventy-seven one-hundredths = 0.77

Sixty-six one-thousandths = 0.066

The product:

0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right.

This is five thousand eighty-two hundred-thousandths.

Eight hundred eighty-eight thousandths = 0.888

Sixty-four ten-thousandths = 0.0064

Set up a long division:

Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.

(Note that leading zeroes have been removed.)

Carry out the long division, making sure you align the decimals:

The quotient of this division is that of the original problem, so the correct choice is 138.75.

Twenty-seven one-thousandths = 0.027

Its square is

Multiply without regard to the decimals first:

0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

This is seven hundred twenty-nine one-millionths.

Fifteen one-hundredths = 0.15

Its cube is

Multiply without regard to the decimals first:

0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

This is three thousand three hundred seventy-five one-millionths.

Although tempting, a calculator is not required to spot the correct answer.

is equal to as it is parts of . And therefore must be slightly different. (It's it actually )

The tenth digit after the decimal point is 3.

When dividing 1 by 3 or 10 by 3, we get repeating 3s. So, there must be a 3 in the tenths digit.