Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 561:

  If x and y are positive integers (x>y), what is the units' digit of (10x ?9y)2 ?

  A. 9.

  B. 7.

  C. 5.

  D. 3.

  E. 1.

  Correct Answer: E

  Try some numbers, x=2, y=1.

  (106 -92)2 = 81. And it will work with any given number under the conditions given.

• Question 562:

  If (R, R2 + 1) is the (x, y) coordinate of a point located on the line: Y = 2X + 4, what Can be the value of the parameter R?

  A. ?.

  B. 2.

  C. 4.

  D. 3.

  E. 1.

  Correct Answer: D

  If the point is on the line then you can plug the coordinate into the equation.

  Y = 2X + 4 R2+1 = 2R + 4 R= 3 or R= -1.

  Therefore the best answer is D.

• Question 563:

  What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?

  A. 60.

  B. 85.

  C. 125.

  D. 225.

  E. It cannot be determined from the information given.

  Correct Answer: D

  First of all, draw the square with the given coordinates. We know only one of the square's sides but it's enough because it is a square and both sides are equal. The area, therefore, is (15 x 15 = 225).

• Question 564:

  P(x, y) is the intersection point between the circle (x2 + y2 = 4) and the line (y = x +2). Which of the following can be the point P?

  A. (1, 2).

  B. (2, 0).

  C. (0, -2).

  D. (-2, 0).

  E. (2, 2).

  Correct Answer: D

  First, draw the circle and the line. The circle is centered at (0, 0) with a radius of 2. You can see that the line and the circle intersect at two points: (-2, 0) and (0, 2). Another way is to insert y = x+2 into the equation of the circle and solve it.

• Question 565:

  What is the area of the rectangle with the following coordinates: (x, y), (10, y), (10, 5), (x, 5)?

  A. 6.

  B. 8.

  C. 12.

  D. 32.

  E. It cannot be determined from the information given.

  Correct Answer: E

  First of all, draw the rectangle with the given coordinates. You can see that only one side of the rectangle is given and not the second, therefore there isn't enough data to answer the question.

• Question 566:

  A(a, b) is the coordinates of the intersection between the lines:

  (x + y –1 = 0) and (4x -2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?

  A. 1.

  B. 2.

  C. 3.

  D. 4.

  E. 5.

  Correct Answer: E

  There is no need to draw the two lines. Multiply equation (1) by 2 and then add the equations to get:

  6x = 7 x = 7/6, y = -1/6.

  Draw a rectangular axis system and mark the point A and B. Complete the two points to a triangle so one

  of sides is 3 and the other is 4, the hypotenuse, which is also the requested length is 5.

• Question 567:

  If X is a root of the equation a3 +8a2 -20a, than which of the following equations Don't have the root X as one of their roots?

  A. X3 + 4X2 -32X.

  B. X2 + 18X + 80.

  C. X2 -12X + 20.

  D. X2 + 5X -14.

  E. X2 + 10X + 16.

  Correct Answer: E

  The original equation is a3 +8a2 -20a, it can be written as a(a -2)(X + 10). The roots are 2,0 and (-10). We are looking for an equation that has none of the same roots. Answer E: X2 -10X +16 = (X + 2)(X + 8) This equation has none of the original roots. All the other answers have one or more of the same original roots.

• Question 568:

  (x, y) are the coordinates of the intersection of the following lines:

  (3x -2y = 8) and (3y + x = 10). What is the value of (x/y)?

  A. 1.

  B. 2.

  C. 3.

  D. 4.

  E. 5.

  Correct Answer: B

  There is no need to draw the lines. There are two equations with two variable that you have to solve. Take the second equation and multiply it by (-3) to get: -9y -x = -30 add this equation to the first and You'll get: -11y = -22 y=2 and x=4. (x/y) is 2.

• Question 569:

  If P is a root of the equation X3 +10X2 + 16X, than which of the following equations have also the root P ?

  A. X2 -10X +16.

  B. X + 8.

  C. X2 +3X -54.

  D. X2 -6X -187.

  E. X2 + 8X - 20.

  Correct Answer: B

  The original equation is X3 +10X2 + 16X, it can be written as X(X + 8)(X + 2). The roots are (-8),0 and (-2).

  We are looking for an equation that has one of the same roots.

  Answer B: X + 8 This equation has the root (-8).

  All the other answers have different roots than the original equation.

• Question 570:

  If A and B are two roots of the equation X2 -.5X -17, then what is the value of A x B?

  A. 15.

  B. -8.

  C. 16.5.

  D. -7.

  E. 22.

  Correct Answer: D

  The roots of the equation are 8.5 and (-2). The multiplication of the roots is equal to (-17).