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Ready4

In the sequence $S$ of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of $S$ ?

(1) The 6th term of $S$ minus the 4th term equals 5.

(2) The 6th term of $S$ plus the 7th term equals 21.

Ready4

The sequence s₁, s₂, s₃, ...s_n,...,s_n,...is such that s_n $= \frac{1}{n} - \frac{1}{n + 1}$ for all integers $n \geq 1$ . If k is a positive integer, is the sum of the first k terms of the sequence greater than $\frac{9}{10}$ ?

(1) $k > 10$

(2) $k < 19$

Ready4

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. If a book is to be selected at random from the books on the shelf, is the probability less than $\tfrac{1}{2}$ that the book selected will be a paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperbacks.

(2) Of the books on the shelf, 15 are written in Spanish.

Ready4

If 2 different representatives are to be selected at random from a group of 10 employees and if $p$ is the probability that both representatives selected will be women, is $p<\tfrac{1}{2}$ ?

(1) More than $\tfrac{1}{2}$ of the 10 employees are women.

(2) The probability that both representatives selected will be men is less

than $p<\tfrac{1}{10}$ .

Ready4

[GMAT-Math-7098-q-GEO]

In the figure shown, lines k and m str parallel to each other. Is x = z?

(1) x = w

(2) y = 180 - w

Ready4

[GMAT-Math-7100-q-GEO]

In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equal area, what are the coordinates of point R?

(1) The coordinates of point P are (0,12).

(2) OP = OQ and QS = RS.

Ready4

The rectangular quilt shown in the figure above has a border of uniform width. What is the area of the portion of the quilt that excludes the border?

(1) The perimeter of the entire quilt is 244 inches.

(2) The width of the border on all sides is 3 inches.

Ready4

A 50% alcohol solution is made by mixing together a 30% alcohol solution with a 60% alcohol solution. What percent of the 50% alcohol solution is made from the 30% alcohol solution?

Ready4

Jose drove his car at an average rate of 100 kilometers per hour on the highway. Some of the distance Jose drove at a rate of 90 kilometers per hour and the rest of the distance he drove at a rate of 106 kilometers per hour. What percent of Jose's drive on the highway was at a rate of 90 kilometers per hour?

Ready4


Cost for a Sweater at a Thrift Shop
Days for Sale in Shop	Percent Markdown
5 − 7 days	10%
8 − 14 days	20%
15 − 21 days	30%
22 − 28 days	50%
Over 28 days	75%

The table above shows the pricing chart for a sweater at a local thrift shop. Suppose the original price for a sweater at the shop was $170. If a consumer purchased the sweater, how many days had it been for sale in the shop?

(1) The discount on the sweater was $51.

(2) If the consumer had waited one more day to purchase the sweater, the sweater would have been discounted an additional $34.

Ready4

Tuition Refund Deadlines
Deadline	Percent of Tuition Refunded
August 23	100%
Sept 7	90%
Sept 14	70%
Sept 21	25%

The table above shows the tuition refund schedule for canceling a class at a local college. If a student cancels a class with an original tuition cost of $3,200, on what day did the student cancel?

(1) The student was refunded $2,240.

(2) If the student canceled the class one day earlier, she would have been refunded an additional $640.

Ready4

The subsets of the set $\{p,q,r\}$ are:

$\{p\}$ , $\{q\}$ , $\{r\}$ , $\{p,q\}$ ,

$\{p,r\}$ , $\{q,r\}$ , $\{p,q,r\}$ ,

and $\{\ \}$ (the empty subset)

How many subsets of the set $\{p,q,r,s\}$ do not contain $s$ ?

Ready4

Running at their respective constant rates, Machine X takes 2 days longer to produce $w$ widgets than Machine Y. At these rates, if the two machines together produce $\frac{5}{4}w$ widgets in 3 days, how many days would it take Machine X alone to produce $2w$ widgets?

Ready4

$3x-y=9$

$|y| \leq 9$

For how many ordered pairs $(x,y)$ that are solutions of the system above are $x$ and $y$ both integers?

Ready4

$\left | y \right |\leq 22$ $5x+y=-20$

For how many ordered pairs $(x,y)$ that are solutions of the system above are $x$ and $y$ both integers?

Ready4

A square patch from a quilt has a square interior surrounded by a border of uniform width. If the ratio of the area of the interior of the patch to the area of its border is 100 to 44, which of the following could be the width, in centimeters, of the border?

I. $2$

II. $4$

III. $11$

Ready4

	$A$	$B$	$C$	$D$	$E$
$A$	0	$y$	52	78	99
$B$	$y$	0	64	$x$	75
$C$	52	64	0	25	31
$D$	78	$x$	25	0	84
$E$	99	75	31	84	0

The table above shows the distance, in miles, by the most direct route, between any two of the five cities $A, B, C, D$ and $E$ . For example, the distance between City $B$ and City $C$ is $64$ miles. What is the value of $x$ ?

(1) By the most direct route, the distance between $A$ and $B$ is three times the distance between $A$ and $D$ .

(2) By the most direct route, the distance between $B$ and $D$ is four times the distance between $A$ and $B$ .

Ready4

If $x$ is an integer, is $x-|x| < 10^x$ ?

(1) $x=0$

(2) $x < 0$