GMAT Data Sufficiency Practice
- Some Interesting questions to test your DS & Quant concepts
MY-GMAT-DS
Geometry
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Basics
1 Land for a pasture is enclosed in the shape of a 6-sided figure; all sides are the same length and all angles have the same measure. What is the area of the enclosed land?
(1) Each side is 8 meter long.
(2) The distance from the center of the land to the midpoint of one of the sides is 4√3 meters.
The best answer choice is (D); Obvious answer was (A)
. M    4    P Facts to remember
.         30º 1. If all 6 sides length are equal and all 6 angles are equal, then the hexagone is made out of 6 equalateral triangles
.       8
2. all angles within the exagone = 60º
.          O 3. The line OP makes the equalateral triangle into 2 true triangles where the inner angles are: 90º, 60º and 30º
60º
4. Then if as said in (1) each side is 8 meter long, then OM = 8 meters as well; then MP = 4 meters; then OP = 4√3 meters; then it is possible to calculate the area of each triangle (area of a triangle = 1/2 base x high) and then of the hexagone itself.
Then the possible answers should be A or D
5. From (2) you can find the same measures - if OP = 4√3 meters then you can theoritically find  the measure of OM and of MP.
The the best possible answer is D
Geometry
Triangles
2 If x, y and z are the lenghs of the three sides of a trinagle, is y > 4
(1) z = x + 4
(2) x = 3 and z = 7
The best answer choice is (D); Obvious answer was (E)
Facts to remember
x z 1. The sum of any two side length of a triangle is always > the the lengh of the 3rd side
2. Therefore; for instance x + y > z
3. Statement (1) implies that x + y > x + 4; then y > 4
y
Then the possible answers should be A or D
4. Statement (2) implies that 3 + y > 7; then y > 4
The the best possible answer is D
3 In the figure shown, QRS is a straight line and line TR biscets < PRS. Is it true that lines TR and PQ are parallel?
(1) PQ = PR
(2) QR = PR
The best answer choice is (B); Obvious answer was (C)
.            P T
.            pº
xº
. qº .        rº xº
Q R S
Facts to remember
1. Since QRS is a straight line, then rº + xº + xº = 180º (or rº + 2xº = 180º)
2. For PQ ║ TR, xº must be = pº
3. From statement (1) you know that qº = rº, but you cannot know if pº = xº
Then the possible answers should be B, C or E
4. From statement (2) you know that qº = pº and then rº + 2pº = 180º
5. If rº + 2xº = 180, then xº = pº, therefore PQ ║ TR
The the best possible answer is B
Geometry
Triangles
4 If each side of the Δ ACD shown has lengh 3 and if AB has lengh 1, what is the area of rgion BCDE?
A. 9 B. 7 √3 C. 9 √3 D. 7 √3 E. 6 + √3
4 4 4 2
C
The best answer choice is (B); Obvious answer was (D)
.     3 Facts to remember
B
1 1. Region BCDE = area of Δ ACD - area of Δ ABE
60º 2. Δ ACD is a equilateral
A F E          D 3. The area of Δ ACD can be calculated as follow:
AF = 3/2 AC √3 x AC = 3 √3 x 3 = 9 √3
CF = 3/2√3 2 2 2 2 4
4. Δ ABE is a right triangle with 30º and 60º angles (since < BAE is 60º)
5. The area of Δ ABE can be calculated as follow:
AB √3 = 1 √3 = √3
2 2 2
6. Therefore, the area of BCDE is:
9√3 - √3 = 9√3 - 2√3 = 7 √3
4 2 4 4 4
The the best possible answer is B
5 A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
A. 4 B. 5 C. 8 D. 9 E. #
.    A The best answer choice is (C); Obvious answer was (E)
.    E Facts to remember
1. AB² = AC² + BC² / 25² = AC² + 7² / AC² = 625 - 49 = 576 / AC = 24
2. EF² = CE² + CF² / 25² = 21² + CF² / CF² = 625 - (24-4)² = 625 - 400 = 225
CF = 15
.  C B F 3. So the answer should be CF - CB / 15 - 7 = 8
AB = EF = 25 The the best possible answer is C
CB = 7
CE = AC - 4
Geometry
Triangles
6 Is ΔMNP isosceles?
(1) Exactly two of the angles, <M and <N, have the same measure
(2) <N and <P do not have the same measure
P The best answer choice is (C); Obvious answer was (A)
Facts to remember
1. If <M = <N, then the triangle is either an isosceles or an equilateral. Since every equilateral is an isosceles, then the answer is yes
M N
Then the possible answers should be A or D
2. If <N = <P, then it could be any type of triangle, therefore the information is not enough to determine if the triangle is an isosceles
The the best possible answer is A
In the figure shown, D is a point on side AC of ΔABC. Is ΔABC isosceles?
(1) The area of triangular region ABD is equal to the area of triangular region DBC
(2) BD ┴ AC and AD = DC
B
The best answer choice is (B); Obvious answer was (E)
Facts to remember
1. As noted in statement (1), you can figure that AD = DC but not if ΔABC is isosceles
.   A D           C Then the possible answers should be B, C or E
2. As noted in statement (2), we can figure that ΔABD and ΔBDC are right triangles and since AD = DC and BD is the common side, so AB = BC and ΔABC is an isosceles
The the best possible answer is B
Geometry
Triangles
7 If the area of triangular region RST is 25, what is the perimeter of RST?
(1) The lengh of one side of RST is 5√2
(2) RST is a right isosceles triangle
R The best answer choice is (B); Obvious answer was (C)
Facts to remember
1. If for instance ST = 5√2, then ½(5√2)h = 25, if it could be proven that it would be the same formula applies on RS so we could know that ΔRST is a right triangle and then the perimetter could be calculated, but the data is not sufficient to determine that
S T
Then the possible answers should be B, C or E
2. Statement (2) shows that for instance RS = ST and that < SRT = < RTS = 45, therefore ½x² = 25 / x = 5√2, therefore based on pythagorean theorem, the perimetter can be calculated
The the best possible answer is B
8 Dan and Karen, who live 10 miles apart, meet at a café that is directly north of Dan's house and directly east of Karen's house. If the café is 2 miles closer to Dan's house than to Karen's house, how many miles is the café from Karen's house?
Karen's house        Café A. 6 B. 7 C. 8 D. 9 E. #
x
The best answer choice is (C); Obvious answer was (A)
    x-2
     10 miles
1 Using the pythagorean theorem, the calculation should be as follow:
Dan's house
x² + (x -2)² = 10²
x² + x² - 4x + 4 = 100
2x² - 4x -96 = 0
2(x² - 2x - 48) = 0
2(a - 8)(x + 6) = 0
a = 8, or a = -6
2 Since it is a distance to calculate, therefore the answer is 8
The the best possible answer is C
Geometry
Quadrilaterals
9 A rectangle is defined to be "silver" if and only if the ratio of its length to its width is 2 to 1. If rectangle S is silver, is rectangle R silver?
(1) R has the same area as S
(2) The ratio of one side of R to one side of S is 2 to 1.
The best answer choice is (E); Obvious answer was (C)
Facts to remember
1. Statement 1 is not sufficient because is rectangle S has one side of 2 and the other of 4 (8m2 area), the other could have one side of 1 and the other of 8 (8m2 area as well).
Then the possible answers should be B, C or E
2. Statement 2 alone is not sufficient because it gives the relations of one side of the rectangle to one side of the other rectangle, not the other side of one to the other.
Then the possible answers should be C or E
3. Because statement 1 and 2 alone are not sufficient for the same reason - one rectangle can be of 4 x 2 and the other 8 x 1, the area is the same (8m2) and the ratio between one side to the other is 1:2 or 2:1, but yet, the second triangle is not silver, but could be if the data is changed with the same logical path.
The the best possible answer is B
10 In the figure shown, two rectangles with the same dimensions overlap to form a shaded region. If each rectangle has perimeter 12 and the shaded region has perimeter 3, what is the total length of the heavy line segments?
a
   c   e
A. # B. # C. # D. 22 E. #
    i
f
           h
b   d
 g
The best answer choice is (C); Obvious answer was (D)
1. [(ab + bd + dc + ca) + (ef + fg + gh + he)] = 24
2. id + dh + hi = 3
3. We need to find what is the length of:
4. ac + ci + bd + ab + ie + ef + fd - Let's call it L
5. L = [(ab + bd + dc + ca) + (ef + fg + gh + he)] - [id + dh + hi]
L = 24 - 3 = 21
The the best possible answer is C
Geometry
Quadrilaterals
11 Is quadrilateral Q a square?
(1) The sides of Q have the same length
(2) The diagonals of Q have the same length
The best answer choice is (C); Obvious answer was (A)
Facts to remember
1. If the sides of Q have the same length it could be either a square or either a rhombus - so statement 1 is not sufficient
Then the possible answers should be B, C or E
2. If the diagonals of Q have the same length it could be either a square or either a rectangle
Then the possible answers should be C or E
3. From the two statements, we can conclude that Q is a square
The the best possible answer is C
12 The surface area of a square tabletop was changed so that one of the dimansions was reduced by 1 inch and the other dimension was increased by 2 inchs. What was the surface area before these changes were made?
(1) After the changes were made, the surface area was 70 square inches
(2) There was 25 percent increase in one of the dimensions
The best answer choice is (D); Obvious answer was (E)
Facts to remember
1. We know before the change it was a square with each side = s. fo after the change, the area of the rectangle = (s - 1)(s + 2).
2. From statement 1, we understand that the area of the rectangle after the change = 70 square inches. So (s - 1)(s + 2) = 70. The result will be of one positive number and one negative number. The positive number will be the length of one side of the before change square and therefore of the area of the before change square.
Then the possible answers should be A or D
3. From statement 2, we know that the increase was only on one side (increase of 2 inches), and that this increase was by 25%. So 0.25s = 2, therefore s = 8 and the area of the square can be determined
The the best possible answer is D
Geometry
Quadrilaterals
13 Is quadrilateral RSTV a rectangle?
(1) The measure of <RST is 90°
(2) The measure of <TVR is 90°
The best answer choice is (E); Obvious answer was (C)
Facts to remember
1. In manner for quadrileteral RSTV to be a rectangle, all its angles have to be =  90°.
2. Statement 1 is not sufficient because it states that one angle (RST) equals 90°. The shape could be either of a rectangle, either a trapezoid with a right angle, either any other quadrilateral with one right angle, either a rectangle
R
S
S
R
         S
R
V T V T V          T
Then the possible answers should be B, C or E
3. Statement 2 alone is the same as statement 1.
Then the possible answers should be C or E
4. Statement 1 + 2 are not sufficient because with 2 right angles, the shape could either look like that:
S
R
S
R
V T V T
or either a rectangle, so therefore, cannot be determined.
The the best possible answer is E
14 The figure shown is composed of 6 squares, each with side s centimeters. If the number of centimeters in the perimeter of the figure is equal to the number of square centimeters in its area, what is the value of s
A. 1 B. 5 C. 2 D. 5 E. 7
3 2 3
The best answer choice is (E); Obvious answer was (B)
Do not make the error of turning the figure into a rectangle for perimeter calculation sakes
1. The area = 6s2. The perimeter = 14s, since the perimeter = the area, therefore 6s2 = 14s. Divide all by s (since s = 0), so 6s = 14 - s = 7/3
The the best possible answer is E
Geometry
Circles
15 The outline of a sign for an ice-cream store is made by placing ¾ of the circumference of a circle with radius 2 feet on top of an isosceles triangle with height 5 feet, as shown. What is the perimeter, in feet, of the sign?
A. 3π + 3√3 B. 3π + 6√3 C. 3π + 2√33 D. 4π + 3√3 E. 4π + 6√3
The best answer choice is (B); Obvious answer was (?)
              O
        2     2 1. In the shown figure, adding the extra material in red, O is the center of the circle = 2. The measure of <AOB = 90° because it cuts off an arc that is ¼ of the circumference (placing ¾ of the circumference of a circle).
               D
A             B 2. So, the right ∆AOB - AB = √22 + 22 = √8 = 2√2
3. Therefore, AD = DB = ½AB = ½ 2√2 = √2
4. In right ∆ CDB, BC = AC = √52 + (√2)2 = √27 = 3√3
5. The length of the curved line = ¾ x (circumference) = ¾ x 2πr = ¾ x 2π x 2 = 3π
          5 ft 6. Therefore, the perimeter of the shape is:
3π + AC + BC = 3π + 3√3 + 3√3 = 3π + 6√3
The the best possible answer is B