Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
Solve GRE practice problems covering Quant (One answer choice and multiple answer choice), Data Interpretation, Text Completion, Sentence Equivalence, and Reading Comprehension Problems.
I have posted a video on YouTube to discuss Positive and Negative Numbers
Attached pdf of this Article as SPOILER at the top! Happy learning!
Following is Covered in the Video
⁍ Types of Numbers ⁍ Zero ⁍ Properties of Positive & Negative Numbers ⁍ Solved Problems
Types of Numbers
Three types of numbers are there in a number line ⁍ Positive Numbers – All numbers to the right of 0 on the number line ⁍ Negative Numbers – All numbers to the left of 0 on the number line ⁍ Zero (neither +ve nor –ve)
Attachment:
img-1.jpg [ 23.04 KiB | Viewed 311 times ]
Zero
⁍ Zero is neither positive nor negative ⁍ Zero is an even number ⁍ For all x ≠ 0, \(x^0\) = 1 ⁍ Division by zero is not defined
Properties of Positive and Negative Numbers
⁍ Addition (P is Positive and N is Negative)
P + P = P, Ex: 2 + 3 = 5 P + N = P or N or 0, Ex1: 3 + (-2) = 1, Ex2: 2 + (-3) = -1, Ex3: 3 + (-3) = 0 N + P = P or N or 0, Ex: Same as above N + N = N, Ex: -2 + (-3) = = -5
⁍ Subtration
P – P = P or N or 0, Ex1: 3 - 2 = 1, Ex2: 2 - 3 = -1, Ex3: 3 - 3 = 0 P – N = P, Ex: 3 - (-2) = 5 N – P = N, Ex: -3 - 2 = -5 N – N = P or N or 0, Ex1: -3 - (-4) = 1, Ex2: -3 - (-2) = -1, Ex3: -3 - (-3) = 0
⁍ Division
P / P = P, Ex: 6/2 = 3 P / N = N, Ex: 6/-2 = -3 N / P = N, Ex: -6/2 = -3 N / N = P, Ex: -6/-2 = 3
⁍ Multiplication
P * P = P, Ex: 2 * 3 = 6 P * N = N, Ex: 2 * -3 = -6 N * P = N, Ex: -2 * 3 = -6 N * N = P, Ex: -2 * -3 = 6
⁍ IF we are multiplying ODD number of Negative numbers then we will get a NEGATIVE number (Assuming they are not getting multiplied with zero)
⁍ IF we are multiplying EVEN number of Negative numbers then we will get a POSITIVE number (Assuming they are not getting multiplied with zero)
⁍ If Product/Ratio of two numbers is positive, then both the numbers will have the SAME sign.
Example : xy > 0 or x/y > 0 => x and y have the SAME sign => Either x > 0 and y > 0 Or x < 0 and y < 0
⁍ If Product/Ratio of two numbers is negative, then both the numbers will have DIFFERENT signs.
Example : xy < 0 or x/y < 0 => x and y have DIFFERENT signs => Either x > 0 and y < 0 Or x < 0 and y > 0
Solved Problems
Q1. Which of the following cannot be the value of x if y/(x-2) = 5 ? A. 1 B. 2 C. 3 D. 4 E. 5
Sol: Denominator cannot be equal to 0 => x - 2 ≠ 0 => x ≠ 2 So, Answer will be B
Q2. Given that a and b are positive, and c and d are negative, which of the following will be positive for sure? (select all possible) A. ab + cd B. ab + acd C. acd + bcd D. abc + d E. c + cd
Sol: A. ab + cd = P*P + N*N = P + P = P = TRUE B. ab + acd = P*P + P*N*N = P + P = P = TRUE C. acd + bcd = P*N*N + P*N*N = P + P = P = TRUE D. abc + d = P*P*N + N = N + N = N = FALSE E. c + cd = N + N*N = N + P = N or P or 0 = FALSE
Sol: Stat A : ab > 0 There are two cases a>0 and b>0 a<0 and b<0 In both the cases we don’t know anything about the sign of d so NOT sufficient
Stat B: ad > 0 There are two cases a>0 and d>0 a<0 and d<0 In both the cases we don’t know anything about the sign of b so NOT sufficient
Combining both the statements we will have two cases (Since we have a common variable “a” in both the statements so we will combine the two statements based on the sign of the common variable) First case of STAT A will be combined with the first case of Stat B and Second case of STAT A will be combined with the second case of Stat B (1) a>0 b>0 d>0 (2) a<0 b<0 d<0 In both the cases bd > 0
So, Together the two statements are SUFFICIENT. So, Answer will be C