GMAT – Quant Exam (Correct Answers)
4^x + 4^-x = 2Correct AnswersTo get reciprocals to equal 2, both must be 1, so x = 0
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?
(1) There exist points A, B, and C, all distinct points on the circle's circumference, such
that the distances QA, QB, and QC are identical.Correct AnswersYes
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?
(2) At least two different diameters of the circle contain point Q.Correct AnswersYes, All
diameters of a circle intersect at the circle's center and nowhere else. Therefore, if Q is
the point of intersection of two or more of the circle's diameters, then Q must be the
center of the circle. The statement is sufficient.
If x is a prime number, what is the value of x?
(2) The average of any x consecutive integers is an integer.Correct AnswersX must be
odd
Then there are an odd number of members in a consecutive set, the mean/median will
be a member of the set and thus an integer (e.g. 5,6,7,8,9; mean/median = 7).
In contrast when there are an even number of members in the set, the mean/median will
NOT be a member of the set and thus NOT an integer (e.g. 5,6,7,8; mean/median =
6.5).
1 / (a+b) < 1/a + 1/bCorrect AnswersIf a and b are positive, then true
Need to test a or b as > 1 as well as 0<(a or b - decimal) <1
If negative, then generally won't be true
|a| + |b| = a + bCorrect Answersa and b must be positive
Rectangle inscribed in a circle -- what is radius circle?Correct Answersradius of circle
equal to half the diagonal
diameter equal to full diagonal, so can use pythagorean theorem to solve
-2^n = ?
(-2)^n=?
If n = 0Correct Answers-2^0 = -1
(-2)^0 = 1
A driver paid n dollars for auto insurance for the year 1997. This annual premium was
raised by p percent for the year 1998; for each of the years 1999 and 2000, the
premium was decreased by 1/6 from the previous year's figure. If the driver's insurance
premium for the year 2000 was again n dollars, what is the value of p?Correct
Answersn * (1+p) * (1-1/6) * (1-1/6) = n
n * (1+p) * 25/36 = n
1+p = 36/25
p = 11/25
,Decreased b y 1/6 = 1 - 1/6
4 ^ 3.5Correct Answers4^3 * 4^.5 = 128
If a number is a perfect square, how many distinct factors does it have?
If a number is a perfect square, sum of distinct factors is?Correct AnswersOdd number
Odd number (1, 2, 4); (1, 3, 9), (1, 2, 4, 8, 16)
Keats Library purchases a number of new books, all in the category of biography; the
library does not acquire any other books. With the addition of the new biographies, the
biography collection of the library amounts to 37.5% of the new total number of books in
the library. If prior to the purchase, only 20% of the books in Keats Library were
biographies, by what percent has the number of biographies in the library increased?
Correct AnswersUse smart numbers, where x = number of books added
(20 + x) / (100 + x) =
x = 28
140% increase from before
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales
tax assessed on the discounted purchase price. If the state sales tax were not
assessed, what percent discount from the item's original retail price, in terms of p, would
result in the same final price?Correct AnswersA * (1 - .1) * (1 + .05) = A * (1 - d)
If n = 10^10 and n^n = 10^d, what is the value of d?Correct Answers10 ^ (10 * (10 ^ 10))
= 10 ^ (10 ^ 11)
A list contains n distinct integers. Are all n integers consecutive?
(1) The average (arithmetic mean) of the list with the lowest number removed is 1 more
than the average (arithmetic mean) of the list with the highest number removed.
(2) The positive difference between any two numbers in the list is always less than
n.Correct AnswersSee it's an INTEGER
(1) Yes (2,3,4,5); mean = 3 or 4 with first or last number removed;
(2) Yes (2,3,4,5) (n = 4, difference of 3); (4,5,6,7,8), n = 5, difference of 4)
Reiko drove from point A to point B at a constant speed, and then returned to A along
the same route at a different constant speed. Did Reiko travel from A to B at a speed
greater than 40 miles per hour?
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B,
was 80 miles per hour.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return
trip.Correct AnswersShould draw out; if yu are given overall mph for whole trip, then you
can almost assume how much time that trip took -- in this scenario the 40mph must be
greater or else it's taking more time to drive one-way then the whole trip
, (1) Suff y the above with real numbers: say the trip is 80 miles long in each direction, so
that the round-trip distance is 160 miles. According to this statement, Reiko took (160
miles / 80 miles/hour) = 2 hours to drive the entire round trip.
Reiko could not have driven from B to A in zero time, so it must have taken her less
than 2 hours to drive from A to B. Therefore, her speed on the trip from A to B must
have been (80 miles)/(LESS than 2 hours) = (40 miles)/(LESS than 1 hour) =
GREATER than 40 miles per hour.
(2) N.S.
In a certain sequence, each term, starting with the 3rd term, is found by multiplying the
previous two terms. What is the difference between the 6th and 3rd terms in the
sequence?
(1) The 1st term is equal to 8 times the 2nd term.
(2) The 4th term is equal to 1.Correct AnswersCan use smart numbers or solve
algebraically
(1) 8x, x, 8x^2, 8x^3, 8^3x^5, 8^4x^8
(2) assume third number is equal to n
so n, 1, n, n --> difference is 0
Can also just asume third number is a random # like 4; so 4, 1, 4, 4
The 1 is the game changer here
The Carson family will purchase three used cars. There are two models of cars
available, Model A and Model B, each of which is available in four colors: blue, black,
red, and green. How many different combinations of three cars can the Carsons select if
all the cars are to be different colors?Correct AnswersUse slot method _____ ____
_____
So you have 8 choices for the first slot, then 6 for the next and 4 for the last one
8*6*4 = 192, BUT you can double count (order doesn't matter -- b/c you can get cars in
different slots and it will be the same -- A Blue, A Black, A Red is the same as A Black,
A Red, A Blue) so need to divide by 3!
8*6*! = 32
What is the median value of the set R, if for every term in the set, Rn = Rn-1 + 3?
(1) The first term of set R is 15.
(2) The mean of set R is 36.Correct AnswersThe set Rn = Rn-1 + 3 describes an evenly
spaced set: each value is three more than the previous.
4^x + 4^-x = 2Correct AnswersTo get reciprocals to equal 2, both must be 1, so x = 0
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?
(1) There exist points A, B, and C, all distinct points on the circle's circumference, such
that the distances QA, QB, and QC are identical.Correct AnswersYes
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?
(2) At least two different diameters of the circle contain point Q.Correct AnswersYes, All
diameters of a circle intersect at the circle's center and nowhere else. Therefore, if Q is
the point of intersection of two or more of the circle's diameters, then Q must be the
center of the circle. The statement is sufficient.
If x is a prime number, what is the value of x?
(2) The average of any x consecutive integers is an integer.Correct AnswersX must be
odd
Then there are an odd number of members in a consecutive set, the mean/median will
be a member of the set and thus an integer (e.g. 5,6,7,8,9; mean/median = 7).
In contrast when there are an even number of members in the set, the mean/median will
NOT be a member of the set and thus NOT an integer (e.g. 5,6,7,8; mean/median =
6.5).
1 / (a+b) < 1/a + 1/bCorrect AnswersIf a and b are positive, then true
Need to test a or b as > 1 as well as 0<(a or b - decimal) <1
If negative, then generally won't be true
|a| + |b| = a + bCorrect Answersa and b must be positive
Rectangle inscribed in a circle -- what is radius circle?Correct Answersradius of circle
equal to half the diagonal
diameter equal to full diagonal, so can use pythagorean theorem to solve
-2^n = ?
(-2)^n=?
If n = 0Correct Answers-2^0 = -1
(-2)^0 = 1
A driver paid n dollars for auto insurance for the year 1997. This annual premium was
raised by p percent for the year 1998; for each of the years 1999 and 2000, the
premium was decreased by 1/6 from the previous year's figure. If the driver's insurance
premium for the year 2000 was again n dollars, what is the value of p?Correct
Answersn * (1+p) * (1-1/6) * (1-1/6) = n
n * (1+p) * 25/36 = n
1+p = 36/25
p = 11/25
,Decreased b y 1/6 = 1 - 1/6
4 ^ 3.5Correct Answers4^3 * 4^.5 = 128
If a number is a perfect square, how many distinct factors does it have?
If a number is a perfect square, sum of distinct factors is?Correct AnswersOdd number
Odd number (1, 2, 4); (1, 3, 9), (1, 2, 4, 8, 16)
Keats Library purchases a number of new books, all in the category of biography; the
library does not acquire any other books. With the addition of the new biographies, the
biography collection of the library amounts to 37.5% of the new total number of books in
the library. If prior to the purchase, only 20% of the books in Keats Library were
biographies, by what percent has the number of biographies in the library increased?
Correct AnswersUse smart numbers, where x = number of books added
(20 + x) / (100 + x) =
x = 28
140% increase from before
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales
tax assessed on the discounted purchase price. If the state sales tax were not
assessed, what percent discount from the item's original retail price, in terms of p, would
result in the same final price?Correct AnswersA * (1 - .1) * (1 + .05) = A * (1 - d)
If n = 10^10 and n^n = 10^d, what is the value of d?Correct Answers10 ^ (10 * (10 ^ 10))
= 10 ^ (10 ^ 11)
A list contains n distinct integers. Are all n integers consecutive?
(1) The average (arithmetic mean) of the list with the lowest number removed is 1 more
than the average (arithmetic mean) of the list with the highest number removed.
(2) The positive difference between any two numbers in the list is always less than
n.Correct AnswersSee it's an INTEGER
(1) Yes (2,3,4,5); mean = 3 or 4 with first or last number removed;
(2) Yes (2,3,4,5) (n = 4, difference of 3); (4,5,6,7,8), n = 5, difference of 4)
Reiko drove from point A to point B at a constant speed, and then returned to A along
the same route at a different constant speed. Did Reiko travel from A to B at a speed
greater than 40 miles per hour?
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B,
was 80 miles per hour.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return
trip.Correct AnswersShould draw out; if yu are given overall mph for whole trip, then you
can almost assume how much time that trip took -- in this scenario the 40mph must be
greater or else it's taking more time to drive one-way then the whole trip
, (1) Suff y the above with real numbers: say the trip is 80 miles long in each direction, so
that the round-trip distance is 160 miles. According to this statement, Reiko took (160
miles / 80 miles/hour) = 2 hours to drive the entire round trip.
Reiko could not have driven from B to A in zero time, so it must have taken her less
than 2 hours to drive from A to B. Therefore, her speed on the trip from A to B must
have been (80 miles)/(LESS than 2 hours) = (40 miles)/(LESS than 1 hour) =
GREATER than 40 miles per hour.
(2) N.S.
In a certain sequence, each term, starting with the 3rd term, is found by multiplying the
previous two terms. What is the difference between the 6th and 3rd terms in the
sequence?
(1) The 1st term is equal to 8 times the 2nd term.
(2) The 4th term is equal to 1.Correct AnswersCan use smart numbers or solve
algebraically
(1) 8x, x, 8x^2, 8x^3, 8^3x^5, 8^4x^8
(2) assume third number is equal to n
so n, 1, n, n --> difference is 0
Can also just asume third number is a random # like 4; so 4, 1, 4, 4
The 1 is the game changer here
The Carson family will purchase three used cars. There are two models of cars
available, Model A and Model B, each of which is available in four colors: blue, black,
red, and green. How many different combinations of three cars can the Carsons select if
all the cars are to be different colors?Correct AnswersUse slot method _____ ____
_____
So you have 8 choices for the first slot, then 6 for the next and 4 for the last one
8*6*4 = 192, BUT you can double count (order doesn't matter -- b/c you can get cars in
different slots and it will be the same -- A Blue, A Black, A Red is the same as A Black,
A Red, A Blue) so need to divide by 3!
8*6*! = 32
What is the median value of the set R, if for every term in the set, Rn = Rn-1 + 3?
(1) The first term of set R is 15.
(2) The mean of set R is 36.Correct AnswersThe set Rn = Rn-1 + 3 describes an evenly
spaced set: each value is three more than the previous.
