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Note for Data Sufficiency - DS By Placement Factory

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Data Sufficiency Workbook By Ramandeep Singh Ram 12/3/2014

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a) Statement (i) ALONE is sufficient, but statement (ii) alone is not sufficient. b) Statement (ii) ALONE is sufficient, but statement (i) alone is not sufficient. c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. d) EACH statement ALONE is sufficient. e) Statement (i) and (ii) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed. (1) If x and y are positive integers, is the following cube root an integer? (i) x = y2(y-1) (ii) x = 2 (2) If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9? (i) w + x + y + z = 13 (ii) N + 5 is divisible by 9 (3) If x and y are distinct positive integers, what is the value of x4 - y4? (i) (ii) (y2 + x2)(y + x)(x - y) = 240 xy = yx and x > y (4) If z = xn - 19, is z divisible by 9? (i) x = 10; n is a positive integer (ii) z + 981 is a multiple of 9 (5) x is a positive integer; what is the value of x? (i) The sum of any two positive factors of x is even (ii) x is a prime number and x < 4 (6) x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7x-1 - 5x? (i) z < 25 and w = 7x (ii) x = 4 (7) x is a positive integer greater than two; is (x3 + 19837)(x2 + 5)(x – 3) an odd number? (i) the sum of any prime factor of x and x is even (ii) 3x is an even number (8) If N, C, and D are positive integers, what is the remainder when D is divided by C? (i) If D+1 is divided by C+1, the remainder is 5. (ii) If ND+NC is divided by CN, the remainder is 5. By Ramandeep Singh Page 2

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(9) What is the value of x? (i) The average (arithmetic mean) of 5, x2, 2, 10x, and 3 is -3. (ii) The median of 109, -32, -30, 208, -15, x, 10, -43, 7 is -5. (10) In 2003, a then-nascent Internet search engine developed an indexing algorithm called G-Cache that retrieved and stored X million webpages per hour. At the same time, a competitor developed an indexing algorithm called HTML-Compress that indexed and stored Y million pages per hour. If both algorithms indexed a positive number of pages per hour, was the number of pages indexed per hour by G-Cache greater than three times the number of pages indexed by HTML-Compress? (i) On a per-hour basis in 2003, G-Cache indexed 1 million more pages than HTMLCompress indexed (ii) HTML-Compress can index between 400,000 and 1.4 million pages per hour (11) If angle ABC is 30 degrees, what is the area of triangle BCE? (i) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC (ii) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12 (12) If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11? (i) x - y is a multiple of 22 (ii) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same (13) If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd? (i) (b # 1) # 2 = 5 (ii) 4 # b = 3 # (1 # b) and b is even (14) If x and y are both integers, which is larger, xx or yy? (i) x = y + 1 (ii) xy > x and x is positive. By Ramandeep Singh Page 3

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(15) A: x2 + 6x - 40 = 0 2 B: x + kx + j = 0 Which is larger, the sum of the roots of equation A or the sum of the roots of equation B? (i) j = k (ii) k is negative (16) Given that A = 3y + 8x, B = 3y - 8x, C = 4y + 6x, and D = 4y - 6x, what is the value of x*y? (i) AB + CD = -275 (ii) AD - BC = 420 (17) After a long career, John C. Walden is retiring. If there are 25 associates who contribute equally to a parting gift for John in an amount that is an integer, what is the total value of the parting gift? (i) If four associates were fired for underperformance, the total value of the parting gift would have decreased by $200 (ii) The value of the parting gift is greater than $1,225 and less than $1,275 (18) If n and k are integers and (-2)n5 > 0, is k37 < 0? (i) (nk)z > 0, where z is an integer that is not divisible by two (ii) k < n (19) What is the area of isosceles triangle X? (i) The length of the side opposite the single largest angle in the triangle is 6cm (ii) The perimeter of triangle X is 16cm (20) For a set of 3 numbers, assuming there is only one mode, does the mode equal the range? (i) The median equals the range (ii) The largest number is twice the value of the smallest number (21) Q is less than 10. Is Q a prime number? (i) Q2 - 2 = P; P is prime and P < 10. (ii) Q + 2 is NOT prime, but Q is a positive integer. (22) John is trying to get from point A to point C, which is 15 miles away directly to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 15 mile route from A to C? (i) Tha ratio of the distance going north to the distance going east is 4 to 3 (ii) The distance traveled north going the direct route is 12 (23) If the product of X and Y is a positive number, is the sum of X and Y a negative number? By Ramandeep Singh Page 4

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