Data Sufficiency
Direction: Each o the following questions is followed by two statements. Mark
- What is the middle number of 7 consecutive whole numbers?
I. Product of number is 702800.
II. sum of the the number is 105.
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Let the 7 consecutive whole numbers be (n ± 3), (n ± 2), (n ± 1), n.
Now i we consider Statement I alone
Product of these 7 integers = 702800
Since 702800 = 24 52 (251)(7), it cannot be the product of 7 consecutive whole numbers. Hence I alone is insufficient.
Now if we consider Statement II alone
Given that their sum = 105 = 7n or n = 15 and then 7 consecutive integers are 12, 13, 14, 15, 16, 17, 18 So, II alone is sufficient.Correct Option: B
Let the 7 consecutive whole numbers be (n ± 3), (n ± 2), (n ± 1), n.
Now i we consider Statement I alone
Product of these 7 integers = 702800
Since 702800 = 24 52 (251)(7), it cannot be the product of 7 consecutive whole numbers. Hence I alone is insufficient.
Now if we consider Statement II alone
Given that their sum = 105 = 7n or n = 15 and then 7 consecutive integers are 12, 13, 14, 15, 16, 17, 18 So, II alone is sufficient.
- If C1 and C2 are the circumferences of the outer and inner circles respectively. What is C1 : C2?
I. The two circles are concentric.
II. The area of the ring is 2/3 the area of greater circle.
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If we look at Statement I
It is given that the circle are concentric. But nothing is given about their dimensions. Hence I alone is not sufficient.
In statement II ratio of area is given hence we can find the required ratio.Correct Option: B
If we look at Statement I
It is given that the circle are concentric. But nothing is given about their dimensions. Hence I alone is not sufficient.
In statement II ratio of area is given hence we can find the required ratio.
- In a general body election, 3 candidates, p, q and r were contesting for a membership off the board.
How many votes did each receive?
I. p received 17 votes more than q and 103 votes more than r.
II. Total votes cast were 1703.
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If we look at Statement I
i = p - 17 and r = p - 103
Hence, we cannot ind how many each received so this statement is not sufficient enough.
Now by considering Statement II alone.
p + i + r = 170
Hence, we cannot find how many each received. so, this statement is not sufficient enough.
Using I sand II together, we get the value of p and the value of q and r.Correct Option: C
If we look at Statement I
i = p - 17 and r = p - 103
Hence, we cannot ind how many each received so this statement is not sufficient enough.
Now by considering Statement II alone.
p + i + r = 170
Hence, we cannot find how many each received. so, this statement is not sufficient enough.
Using I sand II together, we get the value of p and the value of q and r.
- Is 'Ube' positive?
I. a + b is positive.
II. a - b is positive.
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If we look at statement I then we will get
If a = 3 and b = 2, a + b > 0. Here b > 0
If a = 3 and b = -2, a + b > 0. Here b < 0
Hence I alone is not sufficient.
Now if we look at Statement II only then we will get
if a = 3 and b 2, a - b > 0. Here b > 0
If a = 3 and b = -2, a - b > 0. Here b < 0
Hence II alone is not sufficient.
Now by using statements I and II together
If a = 3 and b = 2, a - b > 0 and a + b > 0. Here b > 0
If a = 3 and b = -2, a - b > 0. and a + b > 0. Here b < 0.
Hence I and II together are also insufficient.Correct Option: D
If we look at statement I then we will get
If a = 3 and b = 2, a + b > 0. Here b > 0
If a = 3 and b = -2, a + b > 0. Here b < 0
Hence I alone is not sufficient.
Now if we look at Statement II only then we will get
if a = 3 and b 2, a - b > 0. Here b > 0
If a = 3 and b = -2, a - b > 0. Here b < 0
Hence II alone is not sufficient.
Now by using statements I and II together
If a = 3 and b = 2, a - b > 0 and a + b > 0. Here b > 0
If a = 3 and b = -2, a - b > 0. and a + b > 0. Here b < 0.
Hence I and II together are also insufficient.
- ΔABC and ΔPQR are congruent
I. Area of ΔABC and ΔpPQR are same
II. ΔABC and ΔPQR are right angle Triangles.
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Consider Statement I alone
Given that Area (ΔABC) = Area(ΔPQR) since nothing about the sides or angles is mentioned, we can not say if they are congruent.Hence, I alone is not sufficient.
Consider Statement II alone
ΔABC and ΔPQR are right triangles. Nothing about the sides is given, Hence, II alone is not sufficient. Now using both I and II
Now we have two right angled triangle k with same area we may have different combination as only product of base and height is same. Hence even by using both the statement we can not find the answer.Correct Option: D
Consider Statement I alone
Given that Area (ΔABC) = Area(ΔPQR) since nothing about the sides or angles is mentioned, we can not say if they are congruent.Hence, I alone is not sufficient.
Consider Statement II alone
ΔABC and ΔPQR are right triangles. Nothing about the sides is given, Hence, II alone is not sufficient. Now using both I and II
Now we have two right angled triangle k with same area we may have different combination as only product of base and height is same. Hence even by using both the statement we can not find the answer.
