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GMAT Data Sufficiency Question 45: Distance, rate, and trains

December 22, 2022 Leave a Comment

 
The following GMAT data sufficiency question tests your understanding of applying distance, rate, and time relationships to problems tested on the GMAT.

Question 45:

Trains $A$ and $B$ left stations $R$ and $S$ simultaneously on two separate parallel rail tracks that are $350$ miles long. The trains passed each other at point $X$ after traveling for a certain amount of time. How many miles of the rail tracks had train $A$ traveled when the two trains passed each other?

  1. (1) Up to point $X$, the average speed of train $B$ was $25\%$ less than the average speed of train $B$.
  2. (2) Up to point $X$, the average speed of train $B$ was $60$ mph and it took two and a half hours for train $B$ to arrive at point $X$.
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.

Choice D

Video Explanation

 

GMAT Problem Solving Question 44: Functions

December 13, 2022 Leave a Comment

 
Try the following GMAT Problem Solving question on functions and algebraic manipulation.

Question 44:

The function $f$ is defined by $f(x)=1-x^2$ for all values of $x$. What is $-f(-f(-x))$ ?

  1. $\quad 0$
  2. $\quad x^2-2x$
  3. $\quad x^2+2x$
  4. $\quad x^4-2x^2$
  5. $\quad x^4+2x^2$

Choice D

Video Explanation

 

GMAT Problem Solving Question 43: Sequences and summations

December 6, 2022 Leave a Comment

 
Try the following GMAT Problem Solving question that tests your ability to find the sum of the terms of a sequence.

Question 43:

Let $a_1$, $a_2$, $a_3$, $\ldots$, $a_n$, be a sequence of numbers where $a_1=-2$, $a_2=4$, and for $n \geq 3$, $a_n = \left(\dfrac{a_{n-1}}{a_{n-2}}\right)$. What is the sum of the first $99$ terms?

  1. $\quad -16$
  2. $\quad -12$
  3. $\quad -8$
  4. $\quad -4$
  5. $\quad 0$

Choice B

Video Explanation

 

GMAT Problem Solving Question 42: Sequences and sums

November 30, 2022 Leave a Comment

 
Try the following GMAT Problem Solving question that tests your understanding of identifying patterns in sequences, and using that pattern to add the terms of the sequence.

Question 42:

The terms of a sequence follow the pattern: $-1$, $-2$, $3$, $4$, $-5$, $-6$, $7$, $8,$ $-9$, $-10$, $11$, $12, \ldots \ldots$. If $S$ is the sum of the first $n$ terms of this sequence, then for which of the following values of $n$ is $S=0$ ?

  1. $59$
  2. $75$
  3. $97$
  1. $\quad \textrm{II only}$
  2. $\quad \textrm{I and II only}$
  3. $\quad \textrm{I and III only}$
  4. $\quad \textrm{II and III only}$
  5. $\quad \textrm{I, II, and III}$

Choice B

Video Explanation

 

GMAT Problem Solving Question 41: Circles, arcs, and area

November 23, 2022 Leave a Comment

 
Try the following GMAT Problem Solving question that tests your ability to find areas of intersections of circles.

Question 41:

Three semicircles of radius $1$ are constructed on diameter $\overline{AB}$ of a semicircle of radius $2$. The centers of the small semicircles divide $\overline{AB}$ into four line segments of equal length, as shown below. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?

  1. $\quad \pi-\sqrt{3}$
  2. $\quad \pi-\sqrt{2}$
  3. $\quad \dfrac{\pi+\sqrt{2}}{2}$
  4. $\quad \dfrac{\pi+\sqrt{3}}{2}$
  5. $\quad \dfrac{7}{6}\pi \; – \; \dfrac{\sqrt{3}}{2}$

Choice E

Video Explanation

 

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