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Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing Questions 36–40 (page: 9)

Explanation:

In a parallelogram, the area can be calculated using the formula:
Area = base × height
Here, we are given the lengths of two adjacent sides of parallelogram ABCD: 10 and 16. However, to calculate the area, we also need the height, which is the perpendicular distance between the parallel sides.
Since the height is not provided, we cannot determine the area of the parallelogram exactly from the given information. The area could vary depending on the angle between the sides.

Explanation:

The least common denominator is

Explanation:

9x2 - 4y2 = 1 - 1 = 0

Explanation:

Explanation:

When the positive integer w is divided by 13, the remainder is 1:
w 1 (mod 13)
When w is divided by 15, the remainder is 14:
w 14 (mod 13)
We need to find a value of w that satisfies both conditions.
From the first condition, w 1 (mod 13) can be written as:
w = 13k + 1 for some integer k.
From the second condition, w 14 (mod 13) can be written as:
w = 15m + 14 for some integer m.
Now, set the two expressions for w equal to each other:
13k + 1 = 15m + 14.
13k - 15m = 13.
We need to find integer solutions to the equation 13k - 15m = 13. We can try different integer values for k and check if m is also an integer.
Try k = 1:
13(1) - 15m = 13 13 - 15m = 13 -15m = 0 m = 0.
Thus, k = 1 and m = 0 is a solution. Using k = 1, we find:
w = 13(1) + 1 = 14
Now, check if w = 14 satisfies both conditions:
When 14 is divided by 13, the remainder is 1, which satisfies the first condition.

When 14 is divided by 15, the remainder is 14, which satisfies the second condition.

Thus, w = 14 is a valid solution.