07/22/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #25 (Level: 300-400)

Problem:
In the figure, the coordinates of point V are what?

Solution:
V is 7 units to the right of the origin so the X coordinate is 7. V is 5 units beneath the origin so the Y coordinate is -5. Ergo (7,-5).

Strategy:
The orgin is the point where the horizontal x-axis and vertical y-axis intersect. To the left of the orgin represents negative x-values. To the right of the orgin represents positive x-values. Up from the orgin respresents positive y-values. Down from the orgin represents negative y-values.

07/22/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #24 (Level: 300-400)

Problem:
Fraction

Solution:
1/(1+1/3) – 1/(1+1/2) (simplify both denominators)
= 1/(4/3) – 1/(3/2) (divide numerator by denominator)
= 3/4 – 2/3 (find common denominator)
= 9/12 – 8/12 = 1/12

Strategy:
When adding and subtracting fractions, the first step is always to get a common denominator.
When multiplying fractions, simplify first, then multiply numerators and denominators.
When dividing fractions, keep the first fraction, change the sign to multiplication, and invert the last fraction. Then, multiply.

07/22/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #23 (Level: 300-400)

Problem:
If n is a prime number greater than 3, what is the remainder when n-squared is divided by 12?

Solution:
The fastest way to solve this problem is to pick any prime number larger than 3 (5 being the easiest choice), squaring it, and dividing it by 12. 5-squared = 25 and the remainder when 25 is divided by 12 is 1.

Strategy:
Because only one answer choice can be correct, picking numbers works great for this problem.

You can also use modular arithmetic to solve this problem. Any prime number larger than 3 must be odd, so the remainder when that number is divided by 12 is 1, 5, 7, or 11 (note it can’t be 3 or 9 because then that number would be divisible by 3 and not prime). When you square the number the remainder is 1, 25, 49, or 121, and the remainder of 25, 49, and 121 when divided by 12 are all 1, thus the remainder when the square of a prime number is divided by 12 is 1.

07/22/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #22 (Level: 300-400)

Problem:
Of the five coordinates associated with points A, B, C, D, and E on the number line above, which has the greatest absolute value?

Solution:
The absolute value is greatest for the point farthest from the origin (0), which is point A.

Strategy:
Absolute value is the distance away from the orgin. Because you can never have a negative distance, the absolute value is always positive. For this problem, choose the coordinate that has the greatest distance from the orgin.

07/21/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #21 (Level: 300-400)

Problem:
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Solution:
6 machines produce 270 bottles per minute.
Therefore, 1 machine produces 270 / 6 = 45 bottles per minute.
Thus 10 machines produce 45 * 10 = 450 bottles in 1 minute, and
450 * 4 = 1,800 bottles in 4 minutes.

Strategy:
When working with rate problems, be sure to keep track of units. Your final answer should be the correct unit, in this case, minutes.

07/21/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #20 (Level: 300-400)

Problem:
The ratio of 2 to ⅓ is equal to the ratio of what?

Solution:
Multiply each side of the ratio 2 to ⅓ by 3, yielding 6 to 1.

Strategy:
You can also choose to write the ratio 2 to ⅓ as a fraction: 2 ÷ ⅓ which yields 6.

07/21/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #19 (Level: 300-400)

Problem:
150 is what percent of 30?

Solution:
150 / 30 = 5 *100 = 500%

Strategy:
These types of basic percent problems can be set up using the equation:
Is/Of = %/100
In this question: Is = 150; Of = 30; % = unknown
The equation becomes: 150/30 = x/100

07/21/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #18 (Level: 300-400)

Problem:
If the area of a square region having sides of length 6 centimeters is equal to the area of a rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is what?

Solution:
The area of the square is 6 cm * 6 cm = 36 square-cm.
The area of the rectangle is 2.5 cm * length.
If the areas are equal, then 36 = 2.5 * length.
Therefore, the length = 14.4 cm.

Strategy:
The areas of a square and a rectangle are equal to length * width. For a square, the length and the width are equal. Therefore, the area of a square can be written as side*side.

Also, rather than dividing 36 by 2.5 to get the length, it can be easier to multiply the numerator and denominator by a factor of 1 to eliminate the decimals. Multiplying by 2/2 yields 72 by 5. This can save you valuable time needed for other problems.

07/21/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #17 (Level: 300-400)

Problem:
A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?

Solution:
If half of the rolls were sold by noon, ⅟₂*40 dozen = 20 dozen rolls were sold by noon and 20 dozen rolls remained.
80%, or 0.8 of the remaing rolls = .8*20 dozen = 16 dozen were sold by closing.
Thus, there were 20 dozen – 16 dozen = 4 dozen rolls remaining at closing.

Strategy:
Percents can be written as fractions or decimals. When working with percents, the word “OF” means to multiple. In this problem, half of 40 dozen translates to ⅟₂*40 dozen = 20 dozen. Also, 80% of 20 dozen translates to .8*20 dozen = 16 dozen.

07/21/10  |  POSTED IN GMAT, GMAT Problems&Solutions  |  Comments (0)

GMAT Official Study Guide – PS #16 (Level: 300-400)

Problem:
A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet.  If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

    Solution:
    The capacity (volume) of a rectangular box is calculated as length * width * height (l*w*h).
    So, the equation is l*w*h = 10. 
    Because the new sandbox is twice as long, twice as wide, and twice as high, its capacity is:
     (2*l)*(2*w)*(2*h) = 8*l*w*h.
    Substituting 10 for the value of l*w*h gives
     8*l*w*h = 8*10 = 80.

      Strategy:
      Capacity and volume are interchangeable.  The equation for the volume of a rectangular box is:
      Volume = Length*Width*Height or V=L*W*H

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