zbl

spiderman, when i work it, here's what i get. x - 2y -2 = 0 -> 2y = x - 1 this is an equation of a line that is rising. the two intersection points have been noted by you. 2y = x - 1 => 2y - x + 1 = 0 so we know that (0, -4) is below the line. plug it into the above equation. what do you get? it is :) perhaps, the point is to make it as a line equation where y = ax + b. or rather y - ax - b = 0

then in that case, let me modify my statement. anything to the right of the line is > 0. anything to the left of the line is even if the line is vertical, the equation will be x - 5 = 0 for example. to the right of the line, x will be > 5, eg, 6 which is definitely > 0. to the left of the line, x

let's see ds7, i think both 1) and 2) are insufficent to tell me what the angle ACB. you don't know whether the triangle is isoceles or just a normal triangle. i would say that the answer is E. ds9, a rhombus is a parallelogram with 4 equal sides. from 1), area of a parallelogram is length * height. but you are not told what the height is. from 2), by knowing the diagonal, you don't know much else. even if you have 1) and 2), you cannot figure out one side... so i say the answer is E ds15, from 1), it is insufficient as it does not tell you anything about the 2 triangles. from 2), we only know that one triangle is an equilateral triangle. we don't know about the second triangle. so i also say that the answer is E ds35, answer is C. sum of interior angles is equal to opposite exterior angle. ds36, from 1) you just know the coordinates of M and not N. from 2), you know that OM is equal to 5. but that is still insufficient to figure out what N is...even if you have 1) and 2), you lack information about N. N can be any line from M that touches the x axis. so answer is E

i think perhaps ds45 answer is wrong. (A+B)^2 = A^2 + B^2 -> 2AB = 0 1) now, if a > 0, you are not guaranteed 2AB can be equal to 0. for eg, if B is positve, then (A+B)^2 is definitely != A^2 + B^2. but if B = 0, then the equality holds. 2) now, if b if 1) and 2) holds, then we are always guaranteed that (A+B)^2 != A^2 + B^2 because 2AB is always negative since A > 0 and B answer is C.

i would solve it in a different way. for any line (equation of a line), anything above the line is > 0. anything below the line is so, from 1), by plugging in x = 9 and y = 10, one can figure out from the line equation that the value is > 0. but that is insufficient because we are not sure that it will be in the shaded area or the above above AB but below CD from 2) itself, by plugging in x = 9 and y = 10 into the equation, the value is also > 0. by itself, you still are not sure which area it would lie (same explanation as above) with 1) and 2), you can figure out that (9, 10) lies, which is the shaded area. answer is C

raj, are you familiar with coordinate geometry? a quadratic equation, ie, x^2 + ax + b = 0 can be represented as a U shaped graph. the two points where the U curve cuts the horizontal axis are the two roots of the equation. so 5x^2 - 25x = 0 can be considered a quadratic equation. the two roots are 0 and 5 (when you solve for the equation). now, we know that the U shaped graph cuts the horizontal axis at 0 and 5...anything above the horizontal axis is > 0. anything below the horizontal axis is 0, it has to be the area above the horizontal axis, meaning that x 5 that's the best that i can explain. i find it quite easy if one can visualize the quadratic equation as a U shaped graph.

1) x can be any integer. as such, if x = 3, x is > 2 and 4. 2) 5x^2 - 25x > 0 => 5x (x - 5) > 0. this means that to satisfy this inequality, x 5. as such, you are guaranteed that x does not lie between 2 and 4. B is sufficient. note that a x^2 - ax + b = 0 equality, is represented a U shaped graph, where the two points that it counts the horizontal axis are the two roots of the quadratic equation. if you can visualize such a graph, then you know that if the equation has to be greater than 0, then the area above the horizontal axis should be taken. if the equation has to be less than 0, then the area below the horizontal axis should be taken.

ptan, for Q4), even if one of the digit is 0, you are not guaranteed the the smallest integer is even. eg...consider this sequence, -2, -1, 0, 1, 2 -> smallest integer is -2 and it is even. consider another sequence -1, 0, 1, 2, 3 -> smallest integer is -1, and it is odd.

suchitralingaraj, i think for 2), even though you get x^2 - y^2 = 0, you cannot ascertain that x+y = 0. if x+y = 0, then x^2 - y^2 is also equal to x+y which implies that the statement is true. if you solve for x^2 - y^2 = 0, you get x = -y and x = y. if x = -y, x+y = 0...which makes the statement true. but if x = y, then x+y != 0...which makes the statement false. so 2) is insufficient.

1) insufficient. average speed is (total distance / total time). you do not know at which speed the car was travelling when it had completed half of the distance 2) insufficient. you can only calculate the average speed together...both are still insufficient. just tells you what the average speed is. to get the speed for half of the distance, you need to know the amount of time taken to taken the first half of the distance. this information is not given. answer is E.

yup. shrutig, you got it right. it was the cost of the armchairs that are left in the store

thanks for the rc practices.

i also believe that B is the correct answer. the rest of the answers are wrongly phrased. the "which" is actually referring to the effects of drug and alcohol abuse.

yah, when i saw that question, i also thought that it was weird that the residents can be part of a culture...but apparently, it is proper english to say so.

this is a trick question. the key is that it asked about the number of armchairs in it's stock. one has to assume that some armchairs would be sold...as such, a) is in sufficient since it only gives information about additional costs b) even if you know about total revenue, you don't know what each armchair is being sold at my answer is E. both information are insufficient