Nova's GMAT Math Prep Course

Discover the two formats of GMAT math questions—standard multiple choice and sufficiency—and how the 37-question section emphasizes solving problems over mere mathematical knowledge.

compare the GMAT and SAT math sections, which rely on basic high school algebra and geometry with no proofs, and emphasize solving with short, simple solutions.

Develop mathematical skill beyond what the GMAT tests to perform at your expected level, noting that about 10 percent of course math problems are harder than GMAT problems.

Plug an odd integer, such as 1, into the answer choices to test for even results, and find that only choice d yields an even result (4) and is correct.

Use substitution by testing integer values for n to find which choice cannot be an even integer, eliminating a, b, and c, then confirm d is the answer.

Apply substitution by testing X and Y values to verify which choices yield X/Y > 1, eliminate options, and identify the correct answer as D in this GMAT math example.

Practice substitution to test answer choices by assigning X and Y as perfect squares and evaluating the results in a GMAT substitution problem.

Choose x as an odd integer and y as an even integer, then substitute into the choices to determine which option could be even, noting that the others cannot.

analyze the substitution problem 4 by comparing fractions with cross multiplication and a common denominator; choose k as a perfect square and apply invert-and-multiply, concluding choice e is correct.

Practice solving a substitution problem by testing answer choices, eliminating incorrect options, and confirming that choice e matches the target result in a GMAT math prep context.

Test even values for m in the substitution problem, plug into m+1 and the expressions, eliminate incorrect choices, and confirm choice c with m=0.

solve a substitution problem by taking square roots to find x = 2 or -2, identify x as even, eliminate choices, and select B in nova's GMAT math prep course.

Choose x divisible by eight but not by three, substitute into each answer choice, and eliminate those that yield integers to identify the non-integer option c.

Using p and q as integers, p times q = 2 and p times q plus 2 = 4, 3 is the only integer between 2 and 4, so D.

Select prime numbers x and y, compute x minus y for several pairs, and eliminate choices until the correct substitution problem answer is C.

Learn to plug in the actual answer choices to verify constraints quickly, using digit-sum checks and digit relationships like the tens digit being twice the hundreds digit.

Solve a two-digit number puzzle where the tens digit is twice the units digit, reason through the digits, and use elimination to conclude the answer is D.

Apply substitution by plugging in answer choices to make the expression equal to one. Eliminate incorrect options, confirm D as the correct choice.

Solve a substitution (plugging in) problem by using digit-sum constraints and digit relations, confirming the correct option via elimination, with the 10th digit one third the units digit.

Plug in choices, test for too large or too small, and use backward reasoning from one to eight with the halving pattern to find the answer c.

Apply the substitution (plugging in) method to a GMAT math problem by testing answer choices to see which yields one. Eliminate wrong options and identify B as the correct answer.

Use the pythagorean theorem on a right triangle, solve for height as four, compute the area as one half base times height, yielding six and selecting answer a.

Apply the triangle angle-sum rule to solve for C: 100 and 50 degrees plus C equals 180, so C equals 30.

Solve a GMAT math problem by comparing squared expressions, showing 4x^2 is twice 2x^2 with x ≠ 0, leading to option B.

Use cross-multiplication to compare fractions and determine that 15/16 is greater than 7/9. Apply the technique to all choices and conclude that option a is the largest.

Apply a common denominator by doubling the first fraction, then invert and multiply to combine terms, producing one plus two equaling three and the solution a.

Solve a proportion in GMAT math prep by equating (1/5)/(1/4) to (1/4)/x, apply reciprocals and cross-multiplication, and find x = 5/6.

Identify that A is irrelevant and b controls the expression; raising the negative y to the fourth power keeps the negative sign, yielding -y^4 as the answer.

Solve a GMAT math problem by converting the point (0,4) to a fraction, inverting and multiplying to obtain 100/96, which reduces to 25/24, and the answer is a.

In Nova's gmat math prep course, math notes problem 8 shows that with x = 1/4, 1 over sqrt(x) equals 2 and sqrt(x) equals 1/2, so A is larger.

examine how squaring and square roots affect fractions between zero and one, compare five sixths and six fifths, and determine that statement 3 is false, yielding option a.

Follow an example of substituting x with 2 and y with 3 in the right side of a formula to derive the result and confirm the answer is B.

Explore how find functions simplify a problem with leading terms like z squared, where expressions divided by themselves equal one, leading to answer B.

Apply a two-part function definition to test parity, plug in k=1, and use the inner expression multiplied by 4 to derive 8k-4, identifying the correct choice.

demonstrates evaluating a defined function by substituting x with -pi and then 2pi, simplifying to negative pi, and selecting option c.

Apply a two-part definition to determine whether u and v are odd or even by contradiction, show u is odd and v is even, then compute a difference of five.

This example clarifies that the first element is the base and the second is the exponent, explores negative exponents via reciprocals, and shows which choices are true or false.

Solve a defined functions problem by transforming x^y = -x into x^2 y^2 + y^2 = 0, factor y^2, apply the zero product property, and conclude y = 0.

Apply square-area concepts by recognizing that a square with side x has area x^2, and show that 9^2 divided by 3^2 equals 9, confirming choice b.

Define functions and evaluate the provided formula to determine the result. The expression simplifies to eight, identifying the correct answer as option e.

Use order-based elimination on the answer choices: if the result is less than two, go to d; if greater, go to b. Six yields 18, then 8, so a.

Apply the circle area formula using diameter: since r = D/2, compute pi(D/2)^2 to match the given options, concluding that the correct choice is D.

Identify GMAT math problem where zero sits at X's position, one at Y's position, and A at Z's position, concluding a equals zero by multiplying by negative one, yielding C.

Solve defined functions problem 6 by simplifying and combining like terms, adding x^2 to both sides, then taking the square root to find x = sqrt(2).

Analyze defined functions problem 7 by evaluating star expressions and recognizing squared minus 1 as a difference of squares that factors into plus one and minus one, yielding B.

Define X star Y as X over Y and apply division of fractions by inverting the denominator; derive the expression X Y X over Y Z, selecting the option e.

Factor out x to obtain x times (sqrt(y) minus 2). Apply the zero-product property to see x must be 0 for all y; answer is a.

Work through defined functions in problem 10 by substituting n with 64 and then with 4, applying square roots and basic arithmetic to obtain the final answer.

Use the division by 2 and by 5 to express n as 2q+1 and 5v+3, then equate the expressions and simplify to 2q-5v=2, identifying the correct option.

Lecture tests statements about consecutive integers a, b, c, showing one is divisible by 3 and 4 and that a+b+c is odd; statements one and three are false, answer B.

Nova's GMAT math prep course tests prime pairs for x and y with a difference of 1, then applies elimination to conclude the answer is B.

Explore solving an equation with absolute value and sign changes to determine x equals 3, revealing the correct choice in a GMAT number theory example.

Apply odd and even forms to a GMAT number theory problem, express M as 2x+1 and N as 4v+3, sum them to show an even result, confirming choice C.

primes greater than two are odd, so x times y is odd. therefore the answer is a.

Show that x equals 2z makes 5x a multiple of 10, and similarly 5y a multiple of 10; since 10 is the largest listed option, the answer is E.

Nova's GMAT Math Prep Course presents Number Theory Problem 4, where three consecutive even integers A, B, C yield an average inequality that gives a < -3, selecting choice e.

Analyze a number theory problem with x and y to test prime and even conditions, evaluate x plus five over y, and conclude none of the statements are true.

Identify cube numbers between 2 and 200 (8, 27, 64, 125); determine which are squares, and see that only 64 is a perfect square, so x equals 64.

Solve a number theory problem by plugging in the answer choices, confirm that the digits sum to four and their difference is four, and eliminate options to identify choice C.

This lecture uses the division algorithm to show P = 9Q + 1 and tests parity with Q, concluding that statement 3 is true.

Analyze why P and Q are odd, why their product is odd, why PQ plus 1 is even, and why PQ is not necessarily a multiple of 12.

Identify the smallest prime greater than 53 by testing consecutive numbers and eliminating composites; conclude that 59 is the first prime after 53, option D.

Solve a straight angle problem where a+b=180 and a/b=7/2; substituting gives b=40 and a=140, so the correct choice is C.

Solve for x, z, y, and w using right triangle angle sums and vertical angles, yielding x = 30, z = 60, y = 60, and w = 30.

Learn to apply the exterior angle theorem with a two-variable linear setup: set 2x+60 equal to x+90, solve to find x = 30.

Set up the equation for a cube with edge length e, equating volume e^3 to surface area 6e^2. Factor to e^2(e-6)=0, reject e=0, and conclude the edge length is 6.

Compute the arc length by using the circumference 2 pi r with r = 2 to get 4 pi, then 60° is 1/6 of the circle, giving 2/3 pi.

Compute the shaded area by subtracting the circle area (pi times 1 squared) from the rectangle area (3 times 5 = 15), giving 15 minus pi.

Tackle a two-circle geometry problem: outer radius is three times the inner radius, giving a shaded area of 8π and a ratio to the inner circle area of 8.

Examine how the square's diagonal relates to a circle's radius, given the radius is 2, so SP also has length 2, and conclude that the answer is D.

Identify a right triangle using the pythagorean theorem with hypotenuse 6 and legs y and 3, then solve y^2 = 27 to get y = sqrt(27), answer b.

Solve a geometry problem by comparing circle areas: compute pi r^2 for circles P and Q with radii 1 and 1/2, subtract to find the shaded region, yielding 3/4 pi.

Identify that four arcs with centers at the vertices form a circle of radius three inside a six‑inch square; subtract 9 pi from 36 to get shaded region, answer c.

Explore geometry problems that relate circle area to radius and square side length using square roots and area formulas, as seen in geometry problem 4.

Apply the triangle angle sum to solve a geometry problem. Set angle t to 51 degrees and compute y to be 78 degrees, yielding option D.

Extend horizontal lines to reveal parallel lines and apply interior angle sums. Identify A as 29 degrees via alternate interior angles and B as 90 degrees, totaling 119.

Use parallel lines and corresponding angles to set up 5x + x = 360, apply the 360-degree around a point principle, and conclude x = 60 (option c).

Recognize an isosceles triangle with two 59-degree angles, deduce the third angle is 62 degrees, and conclude the side opposite the largest angle (PQ) is the longest, yielding answer a.

In geometry problem 9, calculate the shaded region by subtracting the smaller circle’s area from the larger circle’s area, giving 3 pi x^2/4.

Compute the area difference between a 6-unit square and a circle of diameter 6 (radius 3, area 9π), yielding 36 minus 9π, divide four shaded regions by two, answer C.

Use angle relationships to derive y equals fifty minus x from a seventy degree setup, then prove fifty minus x is less than thirty five for x greater than fifteen.

Identify parallel lines L and K and the equal corresponding angles; set y = y - 75; solve to find y = 75; select option D.

Calculate the shaded region by subtracting the smaller triangle's area from the larger one's area, yielding 7/8 as the final answer for the geometry problem.

Use radii 1 and 2 to compute circle areas and the shaded region, yielding a 3:1 ratio to the smaller circle.

Apply the pythagorean theorem to an isosceles right triangle to find leg x = sqrt2, then compute shaded area as large triangle area minus small triangle area, yielding 1/2.

Compute triangle areas using base-height relations, deduce base is five times height, derive area 15, then subtract from 40 to obtain 25 for the other triangle; answer is D.

Two right triangles with base 2 and height 4 each have area 4, totaling 8 for the unshaded region, then subtract from the 16 area square to obtain a.

From area 9 pi, determine radius 3, compute circumference 6 pi, use 30-degree angle to get arc length pi/2, and sum to 6 + pi/2.

Use the area formula a = π r^2 to solve for the circle radius, substitute into the circumference relation, and derive r = sqrt(a/π).

Eyeball the geometry to estimate y, confirm it is less than 90 degrees and likely between 65 and 85, then choose D as the correct GMAT answer.

Apply eye-balling techniques to estimate triangle areas using base times height. Approximate the shaded region as half of the larger triangle, guiding you toward the seven-eighths choice (option C).

Determine point B in a square with y-coordinate 4, AB and AO equal 4, so B lies in the second quadrant with x-coordinate -4, giving answer D.

Use the distance formula to show a circle centered at origin has radius three, then confirm a point lies on the circle by its distance to the origin, selecting B.

Apply the slope formula to compute the y-difference over the x-difference from the given values, simplify 2/4 to 1/2, and identify the answer as C.

Identify why the equation is not in slope-intercept form, apply the slope m as rise over run of nine tenths, adjust both sides, and conclude the solution is a.

apply the distance formula to coordinates in coordinate geometry to find ab, ac, and bc, then compute the triangle’s perimeter as ab+ac+bc=5+sqrt(34)+sqrt(5).

Compute the area of a circle centered at the origin with radius three using the formula area equals pi r squared, yielding nine pi.

The coordinates x and y form a right triangle with the origin. Quadrant two placement and axis orientation determine where point P may lie relative to the axes.

Set y to zero to locate the x-intercept, subtract a from both sides, then divide by B to obtain the ratio negative A over B.

Apply the rise-over-run method to compute slope in coordinate geometry from the origin. The lecture explains delta as change and shows a positive slope, concluding the answer is B.

Determine quadrant iii by analyzing coordinate signs; negative x and negative y confirm the answer c.

Derive the line's equation in slope-intercept form using the origin, giving a zero y-intercept. Compute the slope as 1/2 and establish y = (1/2)x.

Analyze the coordinate geometry problem by examining the shaded region in the third quadrant, where both coordinates are negative, and determine that the correct choice is D.

Apply the distance formula to determine if the point (7,7) lies inside a circle centered at the origin by comparing sqrt(98) to the radius 10.

Divides a polygon into triangles and a middle square to compute areas using half base times height, sums them to seven, and identifies the answer as a.

Use distance formula with a right-triangle interpretation to get C = sqrt(2) from legs length 1; the distance between P and 1 is 3 sqrt(2), so the answer is D.