GRE Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing GRE Test Dumps in PDF

Free GRE GRE Test Real Questions (page: 14)

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The circle shown has center O and radius 11. If PR = 12, what is the area of triangle PQR?

Give your answer to the nearest 10. (Enter your answer as an integer or a decimal in the answer box.
Backspace to erase.)

  1. 110

Answer(s): A

Explanation:

Radius of the circle = 11

Diameter (QR) = 2 × 11 = 22

Leg PR = 12

Since QR is the diameter, and PQR is a right triangle, we can use the Pythagorean Theorem to find PQ.



Compute the Area of Triangle PQR:



Area 110



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The sequence a1, a2, a3, ..., ak, ... is defined by a1 = 1 and ak = ak-1 +3 for all integers k 2.
What is the remainder when a2009 is divided by 9? (Enter your answer as an integer or a decimal in the answer box.
Backspace to erase.)

  1. 4

Answer(s): A

Explanation:

The recurrence relation ak = ak-1 + 3 means each term increases by 3 from the previous one. Starting from a1 = 1, we have:

a2 = a1 + 3 = 1 + 3 = 4
a3 = a2 + 3 = 4 + 3 = 7
a4 = a3 + 3 = 7 + 3 = 10
a5 = a4 + 3 = 10 + 3 = 13
...
In general, the k-th term of the sequence is:

ak = 1 + (k - 1) × 3 = 3k - 2

Using the formula ak = 3k - 2, we calculate a2009:

a2009 = 3 × 2009 - 2 = 6027 - 2 = 6025

To find the remainder when 6025 is divided by 9, we perform the division:

6025 ÷ 9 = 669 remainder 4

Thus, the remainder when a2009 = 6025 is divided by 9 is 4.



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The admission price for each child at a certain zoo is of the admission price for each adult. If the admission price for 10 adults and 3 children is $210.80, what is the admission price for each adult? (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)

  1. 17

Answer(s): A

Explanation:

The equation for the total cost can be written as:



To combine these terms, we need a common denominator. The common denominator between 1 and 5 is 5, so rewrite 10x as



Now, combine the terms on the left-hand side:



62x = 210.80 × 5
62x = 1054





What was the range of the average amounts spent per visit at Mall Q in 1998 for the seven age-groups?

  1. $9
  2. $10
  3. $22
  4. $31
  5. $33

Answer(s): E

Explanation:

From the graph, the seven average amounts spent per visit are 39, 51, 60, 70, 72, 62, 48 dollars.
Maximum = 72
Minimum = 39
Range = 72 - 39 = 33 dollars.





For the 45-54 age-group, the average amount spent per visit at Mall Q in 1998 was what percent greater than the corresponding amount for the 25-34 age-group?

  1. 12%
  2. 17%
  3. 20%
  4. 25%
  5. 30%

Answer(s): C

Explanation:

For the 45 - 54 age-group the average spent per visit was $72.
For the 25 - 34 age-group it was $60.
Difference = 72 - 60 = $12.
Percent greater = 12 ÷ 60 = 0.20 = 20%.





For the 18-24 age-group, the average amount spent per person at Mall Q in 1998 was closest to which of the following fractions of the corresponding amount for the 25-34 age-group?






Answer(s): D

Explanation:

Average per person = (average visits per person) × (average amount per visit)







In 2003, what was the ratio of the number of in-store purchases paid for either by check or by credit card to the number of in-store purchases paid for in cash?

  1. 52 to 33
  2. 36 to 31
  3. 33 to 31
  4. 31 to 21
  5. 12 to 11

Answer(s): E

Explanation:

Get the percentages from the graph (for 2003):
Check = 15%
Credit Card = 21%
Cash = 33%
Add check and credit card:
15% + 21% = 36%
So we are comparing:
36 (check + credit)
33 (cash)
Write the ratio:
36 : 33, or 12 : 11





If the distribution of the number of in-store purchases in 2003 by method of payment is to be represented by a circle graph with a radius of 3.2 centimeters, approximately what will be the length, in centimeters, of the area of the sector representing payment by credit card?

  1. 4.2
  2. 4.8
  3. 5.4
  4. 6.0
  5. 6.4

Answer(s): A

Explanation:

From the graph, in 2003:

Credit card purchases = 21% = 0.21
Use arc length formula:
Arc length = (fraction of circle) × (circumference)
Circumference of a circle = 2r r = 3.2 cm 2(3.2) = 6.4 6.4 × 3.14 = 20.1 cm
Arc length = 0.21 × 20.1 4.221 cm



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