GMAT FOCUS PRACTICE EXAM
GMAT FOCUS PRACTICE EXAM SET WITH GUARANTEED ACCURATE ANSWERS
5. The nearest star outside our solar system is approximately 4 x 10^13
kilometers (km) from Earth and our moon is approximately 380,000 km
from Earth. If these distances were scaled down so that the distance from
Earth to our moon was represented by 1 centimeter, then which of the
following is closest to the scaled down distance, in kilometers, from
Earth to the nearest star outside our solar system?A. 10B. 100C. 1,000D.
100,000E. 1,000,000 - ACCURATE ANSWERS✔✔ If we denote the
scaled down distance from Earth to Moon by 1 cm', then we have the
following unit conversion equation:
1 cm' = 3.8 × 10⁵ km
In addition, we need to consider the following unit conversion equations
as well:1 m' = 100 cm'1 km' = 1,000 m'
Now, we simply multiply 4 × 10¹³ km by the corresponding unit
conversion factors until all unnecessary units of measurement cancel
out.
,(4 × 10¹³ km)(1 cm'/3.8 × 10⁵ km)(1 m'/10² cm')(1 km'/10³ m') == 4/3.8
× 10³ km' ≈ 1 × 10³ km' = 1,000 km'
Answer: C_________________
4. A box contains exactly 7 fuses, 3 of which are defective and 4 of
which are not defective. In the bar graph above, the left and middle bars
are the same height and the right bar is half this height. The heights are
intended to represent, respectively, the probabilities of obtaining 0
defective fuses, exactly 1 defective fuse, and 2 defective fuses when 2
fuses are randomly selected without replacement from the box.
However, 1 of the bar heights is incorrect. The correct height is k times
the height shown. Which of the following choices for the bar and the
value of k would result in an accurate representation of the labeled
probabilities? A. Middle bar; k = 1/2B. Middle bar; k = 2C. Left bar; k =
1/2D. Left bar; k = 2E. Right bar; k = 2 - ACCURATE ANSWERS✔✔ 7
fuses (3 def, 4 Ndef) are in the box, from which a random sample of 2
fuses is selected.Left column:P(0 def) = P(Ndef & Ndef) = 4/7 × 3/6 =
2/7Middle column:P(1 def) = P(def & Ndef) + P(Ndef & def) = 3/7 ×
4/6 + 4/7 × 3/6 = 4/7Right column:P(2 def) = (def & def) = 3/7 × 2/6 =
1/7According to the probabilities above, the ratio of the heights of the
columns should be:Left : Middle : Right = 2 : 4 : 1We see that, in the
graph, the heights of the left and right columns are in the correct ratio of
2 : 1. So, the height of the middle column should be changed.If we
double the height of the middle column by multiplying its height by the
factor k = 2, then all three heights will be in the correct ratio.Answer: B
3. For the rental of a certain type of car, rental agency R charges a fee of
$30 per day plus a fee of $0.20 for each mile traveled in excess of 100
miles per day. For the rental of the same type of car, rental agency S
, charges a fee of $65 per day with free unlimited mileage. If a car of this
type is to be rented for 3 days and will be driven the same number of
miles each day, for what total number of miles will the cost of renting
the car from rental agency R be the same as the cost of renting the car
from rental agency S ?A) 352B) 405C) 525D) 750E) 825 - ACCURATE
ANSWERS✔✔ Let us work out the rent by each agency by taking y as
the number of miles per day.1) Rental Agency R: 30+0.20(y-100) per
day2) Rental Agency S: 65 per day.If both are equal =
30+0.20(y−100)=65.......15(y−100)=35.......y−100=175.......y=27530+0.2
0(y−100)=65.......15(y−100)=35.......y−100=175.......y=275
Since we are looking for miles in 3 days => 3*275 = $825E
2. The average (arithmetic mean) of the 5 positive integers, u, w ,x, y,
and z is 14, and u < w <x < y < z. If z is 26, what is the least possible
value of the median of the 5 integers?(A) 3(B) 7(C) 8(D) 9(E) 10 -
ACCURATE ANSWERS✔✔ For the unknown integers,u < w < x < y <
26andu + w + x + y + 26 = 14 × 5 = 70The median is the middle number
in the list of 5 items in ascending order, so:median = xIf the sum of some
variables is given, then we can minimize a certain variable by
maximizing the others.The maximum value of y is 25. Clearly, w cannot
be greater than "median - 1," and u cannot be greater than "median -
2."Of course, according to the given conditions, the median must be an
integer.Let's now concentrate on the sum of the 5 integers:median - 2 +
median - 1 + median + 25 + 26 = 703 × median = 22median = 7.33The
median cannot be less than or equal to 7 because, in this case, the sum of
the 5 integers would be less than 70.If the median, or x, is equal to 8,
then w can be equal to 7, and u can be equal to the rest, or 70 - 26 - 25 -
8 - 7 = 4.
