Solutions and explanations to GMAT problems in sample 1 .
## Solution to Question 1If L is the length and W the width of the rectangle, the perimeter P is given byP = 2 L + 2 W = 120 The equation 2 L + 2 W = 120 has two unknown and can only be solve using the width W = 20. Both the perimeter and the width are needed to answer the question. Answer C
## Solution to Question 2To find the value of x, the values of t, z and w are needed. Z is given. Also z can be used to find w using z = 2w + 1 as follows- 5 = 2w + 1 y is needed to find t using y = 2 t - 1 as follows 3 = 2 t - 1 Both statements (1) and (2), together, given above are needed to answer the question. Answer C
## Solution to Question 3The area of a right triangle is given by(1/2) × length of leg1 × length of leg2 Being an isosceles triangle the length of the two legs are equal to 10 and the area may be calculated using statement (1) only. If h is the length of the hypotenuse and x is the length of leg of the isosceles right triangle, by Pythagorean theorem we have x ^{2} + x^{2} = h^{2}
The above equation may be used to find x ^{2} which in turn may be used to find the area of the triangle. Hence statement (2) may also be used, on its own, to answer the given question.
Since each statement, on its own, may be used to answer the question, the answer is D
## Solution to Question 4Statement (1) means either x = y or x = - y and cannot be used to answer the question. Statement (2) means that x and y have the same sign, since their product is positive, but cannot be used to answer the question. If we now use statement (1) and (2) together we can answer the question and say x = y.Answer C
## Solution to Question 5Let x, y and z be the number of Maths, Biology and Geography books respectively. We need to find the total number of books which is given byx+ y + z "There are 150 more Geography than Maths books" is translated as follows z = x + 150 The ratio of Maths to Biology books is 5:7 could be written as x / y = 5 / 7 It is clear that the two equations found above are not enough to find the sum x + y + z The ratio of Biology to Geography 7:8 could be written as y / z = 7 / 8 We now have 3 equations with 3 unknown and the question can be answered. So both statement (1) and (2) are necessary and no one on its own is sufficient to answer the question. Answer C
## Solution to Question 6Statement (1) could be used to write(x + y) ^{2} = 4^{2}
Expand the left side x ^{2} + y^{2} + 2xy = 16
At this point we cannot find x ^{2} + y^{2} because the product xy is unknown. Statement (2) can be used to write
x y = 2 which can therefore be used in the equation x ^{2} + y^{2} + 2xy = 16 to find x^{2} + y^{2}. So both statements (1) and (2) are necessary to answer the question but none on its own is sufficient to answer the question.Answer C
## Solution to Question 7x is one of two unknown in a given system of equations and therefore both statements are necessary to answer the question and none on its own is enough to answer the question.Answer C
## Solution to Question 8No information is given as to what kind of quadrilateral is the question about. Statements (1) and (2) together are not sufficient to answer the question asked, additional information is needed.Answer E
## Solution to Question 9Since m and n are positive, we can write|m + n| = m + n = 14 Since m is less than n, m - n < 0 Hence |m - n| = -(m - n) = 2 Multiply m + n by -(m - n) (m + n)(-(m - n)) = - (m ^{2} - n^{2}) = 14 * 2
Both statements are necessary to answer the question and none on its own is sufficient to answer the question. Answer C
## Solution to Question 10Statement (1) gives the value of the surface area S which can used to find the radius r using the formulaS = 4 Pi r ^{2}
and r can be used to find the volume V of the sphere using the formula V = (4/3) Pi r ^{3}
statement (2) can be used to find the volume using again the above formula. Hence each statement alone is sufficient to answer the question asked. Answer D
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