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GRE Practice of the Day - 29th June 2020

  1. x is a positive integer such that 2x is a factor of 1,000.

QUANTITY A

The greatest value for x

QUANTITY B

9
  1. Quantity A is greater
  2. Quantity B is greater
  3. The two quantities are equal
  4. The relationship cannot be determined from the information given

Solution: There is an obvious and easy to avoid trap here.
29 represents the highest power 2 can take such that it is less than or equal to 1000.
210 equals 1024 so 29 is the largest number that’s a power of 2 and lesser than 1000. The question however doesn’t ask that. You need to find the largest number that can evenly divide 1000 and that number must also be a power of 2.
X = 3 because the largest power of 2 that can divide 1000 is 23 = 8.

  1. Compare Quantity A and Quantity B and select one of the following four answer choices:

QUANTITY A

4 260 

QUANTITY B

4
  1. Quantity A is greater
  2. Quantity B is greater
  3. The two quantities are equal
  4. The relationship cannot be determined from the information given

Solution: Though you will get a calculator on the GRE test you should use it minimally to avoid wasting time. In this case you can use the GRE test calculator.
You can use it to find the fourth root of 260 (which will be in 2 operations because you only have the square root function, so you will have to square root 260 and then square root whatever value you get)) or use it to find the fourth power of 4.
The simple thing would be to find the fourth power of both quantities
A = 260 and B = 44= 256

  1. If x is a positive integer, what is the remainder when 34x + 2 is divided by 8?

Solution: Write 34x + 2 as 34x x 32.

In other words 81x x 9 is divided by 8.

81 divided by 8 leaves a remainder of 1 so 81x divided by 8 will leave a remainder of 1x = 1.

9 divided by 8 also leaves a remainder of 1 so 81x x 9 will leave a remainder of 1 x 1 = 1.

  1. At a certain factory, there are 3/5 as many managers as there are supervisors, and each manager earns 4/3 as much money per week as each supervisor does. In any given week, the total amount earned by managers is what percent of the total amount earned by supervisors?

Solution: Since we don’t know the numbers or the wages but we know the ratios, let us make our lives easier by working with whole numbers instead of fractions.
Let the number of supervisors be 5, so the number of managers will be 3/5 of 5 = 3.
Further let the supervisor make $3 per week so the manager must make 4/3 of that = $4.
Supervisors make 5 x 3 = $15 per week.
Managers make 3 x 4 = $12 per week.
The question asks, “In any given week, the total amount earned by managers is what percent of the total amount earned by supervisors?” OR in other words, it asks “$12 is what % of $15?”.
12/15 x 100 = 80%.

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Q. If the function f(x) is defined as f(x) = 3(x + 1) + 7, then f(a − 2) =

  1. 3a + 5
  2. 3a – 9
  3. 3a + 10
  4. 3a – 4
  5. 3a + 4
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