All You Wanted to Know About GRE Quant Arithmetic

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There is a saying in Mathematics that, “Arithmetic is the Queen of Mathematics”, because of its high importance. Similarly, in GRE Quant, Arithmetic is very important; one can easily say that in GRE, arithmetic comprises approximately 40 to 50 percent of the Quant questions.



What is tested in Arithmetic?


What is tested in Arithmetic can be split into three broad buckets:

   • Numbers and Operations

   • Ratio and Percentages

   • Rates


I) Numbers and Operations


A student who is writing GRE must be very clear about Real numbers as it is a  basic concept one will need to solve any GRE question.


Questions will be based on properties of integers, fractions, Powers and Roots of a number, and Number line (Real Line).


Properties of integers questions test your skills at:

   • Division algorithm

   • Divisibility Rules

   • Remainder Rules

   • Prime factorization

   • Factors and Multiples


Fractions questions test your skills at:

   • How to compare fractions

   • Terminating fraction and Non-terminating fraction.


Exponents and roots questions test your skills in:

   • Basic exponent rules

   • Cyclicity of powers (unit’s place of number when raised to an integer power)

   • Maximum power of an integer in a factorial


Number line questions mostly test the decimals values, distance between two numbers, and total number of elements between two integers.



Sample Questions


   1. What is the unit’s digit of (16782345) * (30753847) ?

   1. 0

   2. 2

   3. 5

   4. 6

   5. 8




Here, one must know the cyclicity patterns of each and every digit.

We only we need to find 82345 * 53847

8 – follows a 4 cycle pattern – that is the units place ends with either 8,4,2,6.

82345  = 82344+1 = units place is 8.

5any  = always ends with 5. Five raised to any integer (positive) power always ends with 5.

8 * 5 = 40. So the answer is A.



II) Ratio and Percentages:


Ratios and Percentages will also be tested in Algebra and Geometry.

In Arithmetic, the questions will be based on Ratio and Proportion, Percentages, and Profit and loss.


Ratio and Proportion questions test your skills at:

   • Finding the actual value when given a ratio

   • Comparing two ratios and multiple ratios

   • Constructing an equation using ratios


Percentages questions test your skills at:

   • Converting a fraction to a percentage

   • Successive percentage change

   • Percent increase/ Decrease.

   • Simple Interest and Compound Interest


Profit and loss questions test your skills at:

   • Cost Price, Selling Price and Marked price

   • Successive discounts

   • Increasing/Decreasing one price with respect to another.


Sample question:


A used car dealer sold one car at a profit of 25% of the dealer’s purchase price for that car, and sold another car at a loss of 20% of the dealer’s purchase price for that car. If the dealer sold each car for $20,000, what was the dealer’s total profit or loss, in dollars, for the two transactions combined?

  1. 1000 profit

  2. 2000 profit

  3. 1000 loss

  4. 2000 loss

  5. 3334 loss




A dealer sold one car at a profit of 25% of the dealer’s purchase price for that car,

let’s say  C1, for $20,000.

C1∗1.25 = 20,000.


Profit = Selling price−purchase price


A dealer sold another car at a loss of 20% of the dealer’s purchase price for that car,

let’s say  C2, again for $20,000.



Loss = purchase price−selling price


Overall loss is 5,000-4,000=1,000,

Hence, the answer is C.



III) Rates:


Rates will be among those topics where you can expect hard questions.


Rates questions test your skills at:

   • Time and Work

   • Time, Speed and Distance

   • Average Speed

   • Group and Independent work.

   • Relative Speed (speed of one object when compared to that of another object).


Rates questions, can also be solved using Back Solving (using the answer choices) and by Plugging in the values.


Sample questions:


Ben and Sam set out together on bicycles traveling at 15 and 12 miles per hour, respectively. After 40 minutes, Ben stops to fix a flat tire. If it takes Ben one hour to fix the flat tire and Sam continues to ride during this time, how many hours will it take Ben to catch up with Sam, assuming he resumes his ride at 15 miles per hour?

  1. 3

  2. 3.33

  3. 3.5

  4. 4

  5. 4.5




The best way to solve a Time, Speed and Distance question is by picturing it.

The distance between Ben and Sam after 40 minutes (2/3 hours) is (distance) = (time)(speed) = 2/3*(15-12) = 2 miles (Ben will be 2 miles ahead of Sam).

In one hour, Sam covers 12 miles, so after an hour, Sam will be 12 – 2 = 10 miles ahead of Ben.

To catch up, Ben will need (time) = (Relative distance)/(Relative speed) = (Distance between them)/( Difference of their speeds-same direction)= 10/(15-12) = 10/3 hours.

So, the answer is B.


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