GRE Numeric Entry (NE) Practice Questions

Written Explanation

We need to determine the percentage of dinosaur fossils that are more than 75 million years old but less than 110 million years old.

77 percent of the dinosaur fossils are more than 75 million years old.
This implies that 100 – 77 = 33 percent of all the dinosaur fossils were 75 million or less than 75 million years old.

90 percent of the dinosaur fossils are less than 110 million years old.
This implies that 100 – 90 = 10 percent of all the dinosaur fossils were 110 million or more than 110 million years old.

The percentage of dinosaur fossils that are more than 75 million years old but less than 110 million years old
= (Total percent) – (Percent of dinosaur fossils that were 75 million or less than 75 million years old) – (Percent of dinosaur fossils that were 110 million or more than 110 million years old)
= 100% – 33% – 10%
= 67%

67 is the correct answer. 

Written Explanation

MB = 5
NB = 3
AB = AM + MB = 10 + 5 = 15
DB = DN + NB = 6 + 3 = 9
We need to determine the area of the quadrilateral AMND.

Triangle ADB is a right-angled triangle.
AB² = AD² + DB²
AD² = AB² – DB²
AD² = 15² – 9²
Solving for AD, we get;
AD = 12

Similarly, triangle MNB is a right-angled triangle.
MB² = MN² + NB²
MN² = MB² – NB²
MN² = 5² – 3²
Solving for MN, we get;
MN = 4

Area of quadrilateral AMND
= Area of triangle ADB – Area of triangle MNB
= [(1 / 2 ) × DB × AD] – [(1 / 2 ) × NB × MN]
= [(1 / 2 ) × 9 × 12] – [(1 / 2 ) × 3 × 4]
= 54 – 6
= 48

Hence, the area of quadrilateral AMND is 48.

48 is the correct answer.

Written Explanation

(3m)(8n) = 816
24mn = 816
mn = 34
We need to determine the value of m + n.

Since m and n are integers, {2, 17} is the only set of possible values for m and n.
Hence, m + n = 2 + 17 = 19.

19 is the correct answer. 

Written Explanation

Let the number of shares owned by Jane and Sylvie in 2018 be x.
In 2019, since Jane increased the number of shares she owns by 25 percent, the new number of shares owned by Jane is 1.25x.
Similarly, since Sylvie decreased the number of shares she owns by 30 percent, the new number of shares owned by Sylvie is 0.7x.

Required percentage 
= [ (Number of shares owned by Jane in 2019) – (Number of shares owned by Sylvie in 2019) / (Number of shares owned by Sylvie in 2019) ]
= (1.25x – 0.7x) / (0.7x)
≈ 78.57%
≈ 78.6%

Hence, at the end of 2019, the number of shares owned by Jane was 78.6% higher than the number of shares owned by Sylvie.

78.6 is the correct answer.

Written Explanation

We need to determine the amount of time it would take the two machines, working simultaneously, to bottle x bottles of honey.

The most efficient bottling machine in a bottling plant can bottle x bottles of honey in 30 minutes.
This implies that in 1 minute the most efficient bottling machine can bottle x / 30 bottles of honey.

Similarly, the least efficient bottling machine in a bottling plant can bottle x bottles of honey in 45 minutes.
This implies that in 1 minute the least efficient bottling machine can bottle x / 45 bottles of honey.

If these two machines work simultaneously, they can bottle ( x / 30 ) + ( x / 45 ) = (x / 18) bottles of honey.

Hence, it will take 18 minutes for the two machines, working simultaneously, to bottle x bottles of honey.

18 is the correct answer.

Written Explanation

We need to determine the number of salespeople in Mira’s company.

Mira was ranked the 4th highest-performing salesperson. This implies that 3 salespeople ranked above Mira.

If 2 of the salespeople ranked below Mira had outperformed her, there would have been 13 salespeople ranked below Mira.
This implies that there are currently (13 + 2) = 15 salespeople ranked below Mira.

The total number of salespeople in Mira’s company
= 3 (salespeople ranked above Mira) + 1 (Mira) + 15 (salespeople ranked below Mira)
= 19 salespeople.

19 is the correct answer.

Written Explanation

We need to determine the number of possible 3-digit positive integers that are even and do not contain any prime digits.

2, 3, 5, and 7 are prime numbers.
The numbers with numbers 0, 2, 4, 6, or 8 as the units digit are even numbers.

Since the integer is even and does not contain any prime digits,
There are 4 possibilities for the units digit: {0, 4, 6, 8}
There are 6 possibilities for the tens digit: {0, 1, 4, 6, 8, 9}.
There are 5 possibilities for the hundreds digit: {1, 4, 6, 8, 9}

The total number of possible 3-digit integers that satisfy all the conditions = 4 × 6 × 5 = 120.

120 is the correct answer. 

Written Explanation

Let the units digit of the two-digit positive integer be u.
Let the tens digit of the two-digit positive integer be t.
We need to determine the value of the two-digit positive integer.

Since the units digit is 4 more than twice the tens digit, u = 2t + 4          (Equation I)
Since the product of the digits is 16, ut = 16          (Equation II)

Intuitively:
There are only 3 possible combinations of u and t that satisfy Equation II: {(u = 2, t = 8), (u = 4, t = 4), (u = 8, t = 2)}
Out of these 3 combinations, only (u = 8, t = 2) satisfies Equation I.
Therefore, u = 8 and t = 2.

Mathematically:
Substituting the value of u from Equation I into Equation II,
(2t + 4)t = 16
2t² + 4t = 16
t² + 2t = 8
t² + 2t – 8 = 0
t² + 4t – 2t – 8 = 0
(t – 2)(t + 4) = 0
Therefore, t = 2 or t = –4.
Since the value to t cannot be negative,
t = 2

Substituting the value of t in Equation II,
2u = 16
u = 8

Hence, the two-digit positive integer is 28.

28 is the correct answer.

Written Explanation

Let the number of students who own no automobile be n.
Since there are half as many students who own a motorcycle as students who own no automobile, the number of students who own a motorcycle = n / 2 .
The total number of students in the survey = 2,700.
We need to determine the value of n.

Since 4 / 9 of the students own a car, the number of students who own a car = ( 4 / 9 ) × 2,700 = 1,200.

The number of students who own a car + The number of students who own a motorcycle + The number of students who own no automobile = The total number of students in the survey.
1,200 + ( n / 9 ) + n = 2,700
Solving for n, we get;
n = 1,000

Hence, the number of students who own no automobile is 1,000.

1000 is the correct answer.

Written Explanation

The probability that it will rain on Christmas = 0.3.
The probability that it will rain on New Year’s Day = 0.4.
We need to determine the probability that it will not rain on either day. 

The probability that it will not rain on Christmas 
= 1 – (The probability that it will rain on Christmas)
= 1 – 0.30
= 0.7

The probability that it will not rain on New Year’s Day 
= 1 – (The probability that it will rain on New Year’s Day)
= 1 – 0.4
= 0.6

The probability that it will not rain on either day
= (The probability that it will not rain on Christmas) (The probability that it will not rain on New Year’s Day)
= (0.7 × 0.6)
= 0.42

Hence, the probability that it will not rain on either day is 0.42. 

0.42 is the correct answer.