Decimal Operations - GRE Quantitative Reasoning

To solve this problem, subtract from both sides of the eqution,

Therefore, .

If you're having trouble subtracting the decimal, mutliply both numbers by followed by a number of zeroes equal to the number of decimal places. Then subtract, then divide both numbers by the number you multiplied them by.

To solve, you need to do some algebra:

Isolate x by adding the 4.150 to both sides of the equation.

Then add the decimals. If you have trouble adding decimals, an effective method is to place one decimal over the other, and add the digits one at a time. Remember to carry every time the digits in a given place add up to more than .

To solve for , first add to both sides of the equation, so that you isolate the variable:

Then, add your decimals, and remember that .

To solve, first add to both sides of your equation, so you isolate the variable:

Then add the decimals together:

To solve, first add to both sides of the equation:

Then add the decimals together:

To solve, first divide both sides of the equation by , leaving you with:

Then simply divide the decimals, which will yield your answer:

.

If you have trouble dividing the decimals, you can multiply both of the numbers by one followed by a number of zeroes equal to the number of digits beyond the decimal point (one hundred, in this case), then divide, then divide your result by the same number (one hundred again).

To solve, first divide both sides of the equation by :

To do this division, you can divide as normal, or if you are having trouble, you can multiply both numbers by 10 to eliminate the decimal:

To solve, first divide both sides of the equation by so you isolate the variable:

Then, divide the decimal--if you have trouble doing so, remember that you can multiply both numbers by to eliminate the decimal, and then divide as normal:

To solve, first divide both sides of the equation by so you can isolate the variable:

Now divide. If you have trouble dividing decimals, you may multiply both dividend and divisor by to eliminate the decimal and divide normally:

To solve, first divide both sides of the equation by so you isolate your variable:

Then, divide the decimals. If you have trouble with this, you can multiply both numbers by to eliminate the decimals and then divide normally:

0.7 * 0.7 = 0.49

Trick: do the numbers without the decimals (7*7)

49; move the decimal of the answer the total number of spaces per each number (one for each 0.7)

0.49

In this question, simply take the percentage of each group that owns a minivan and compare the values. For minivans we look at the middle row which we recognize as a percent that must be converted to a decimal. Acknowledge that there's a different number of people between the groups A and B:

Group B: 0.15(5000) = 750

Group A: 0.22(3500) = 770

750 – 770 = –20; thus, group B has 20 fewer people who own minivans than group A.

We must recognize that if x and y are both between 0 and 1, then they must be fractions (decimals). To determine their relationships, we can substitute values for x and y. Let's have and (because y must be greater than x).

If x and y are both between 0 and 1, then xy is also between 0 and 1 (though smaller than either x or y individually).

The value of (xy)2 will be less than (xy), since squaring any number between 0 and 1 gives a smaller result.

Finally, is largest, since dividing a larger number by a smaller one gives a result greater than 1.

Note that the substituted values for x and y were purely hypothetical; any values that satisfy the given inequality could be used.

Set the equation up as

Solve for , which equals

or

Therefore the percent sales tax is:

Use the values of .5 and 2 as possible x values. If x = 2, Quantity A is positive and greater, but if x = .5, Quantity A is negative and therefore smaller. As such, the relationship cannot be determined.

Make sure to follow the order of operations. Begin by combining all terms inside the parentheses:

Convert the fraction to a decimal and once again complete the operations inside the parentheses:

The answer is .

To solve for , subtract from both sides of the equation. , therefore, .

If you have trouble subtracting the decimals, you can multiply both of them by to get whole numbers, then subtract as normal, then divide your result by .