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Quant Data Sufficiency Questions for IBPS PO 2021 | Download Data Sufficiency PDF for IBPS Clerk Mains 2021 at Smartkeeda

Directions: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:
1
While writing first N natural numbers, I missed one number. What is the number that I missed?
 
Statement I : The sum of all the natural number which I wrote, is 320. 
 
Statement II : The digit I missed is an odd number. 
 
Statement III : if I had not missed the number then sum would have been 325. 
» Explain it
B
Sum of the first N natural number =  n (n + 1)
2

Let I missed number x then,

From the statement I :

N (n + 1)  – x = 320, N(N + 1) – 2X = 640
2

Product of two consecutive number – 2x = 640

Product of two consecutive number = 640 + 2x

It means, the Product of two consecutive number should be greater than 640

The first possible number = 25 × 26 = 650 = 640 + 2x

it means, the number of terms = 25 = n

and x = 5

If we take n = 26 then

26 × 27 = 702 = 640 + 2x

In this case, x = 31 which is greater than 26 therefore only n = 25 is possible

Hence, we can conclude our answer to this statement.

From the statement II :

we can conclude only the condition that the number I missed was an odd number. To this statement it is not possible to get a unique answer.

From the statement III :

we can conclude the sum of all the number without missing any number but we don’t have any information about the number I missed.

Hence, option B is correct.
2
A triangle is circumscribed by a circle. What is the perimeter of the triangle? 
 
Statement I : The circumference of the circle is 28π cm. 
 
Statement II : The largest side of the triangle is diameter of the circle. 
 
Statement III : The triangle is an isosceles triangle. 
» Explain it
D
From the statement I : we can conclude, the radius of the circle = 14 cm therefore the diameter of the circle = 28 cm.
 
From the statement II : we can conclude that the largest side of the triangle = 28 cm and it is circumscribed by a circle therefore it will be a right - angled triangle because diameter make 90 degree at any point on the circumference. 
 
From the statement III : we can conclude that it is an isosceles triangle. 
 
If we combine all the statements then we can conclude that we need to find the perimeter of an isosceles right – angle triangle the hypotenuse of which is 28 cm (the diameter of the circle). 
 
By the Pythagorean theorem, we can get our unique answer. 

Hence, option D is correct.
3
What is the respective speed of the two trains, A and B of length 150 meters and 175 meters respectively. 
 
Statement I : They take 5 seconds to cross each other when they are running in opposite direction.  
 
Statement II : They take 65 seconds to cross each other where running in the same direction.  
 
Statement III : The sum of their speed is 65 m per sec. 
» Explain it
A
From the question, the length of train A = 150 meters and let the speed = x m/sec
 
And the length of train B = 175 meters and the speed = y m per sec 
 
From the statement I, distance = speed × time 
 
325 = (x + y) × 5 
 
x + y = 65 ------ (i) 
 
From the statement II, x – y = 5 ------- (ii) 
 
If we combine the statement I , and II and solve the equation then we can get our answer. 
 
From the statement III, x + y = 65 ------- (iii) 
 
If we combine statement II, and III then we can get our answer. 
 
Hence, option A is correct.
4
A sum of Rs. 229 was divided among a, b, and c. What is the difference between the share of a and that of b?
 
Statement I : The share of c is 40% less than the sum of the share of a and b. 
 
Statement II : The difference between b’s share and c’s share is Rs. 4. 
 
Statement III : The share of c is greater than the share of b.  
» Explain it
D
From the question, a + b + c = 229 ........ (i)
 
From the statement I, c = 60% (a + b)  = > 3a + 3b = 5c ........ (ii)
 
Multiply equation (i) by 5 and add both the equation then we can get a + b but we cannot find a – b.
 
From the statement II,
 
|b – c| = 4 [ The modulus sign is given because we do not know whether b > c or c > b ]
 
From the statement III, we conclude that c > b
 
Therefore, by combining statement II and III
 
c – b = 4 ........... (III)
 
Put the value of c in the equation I, a + 2b = 225 ........(iv)
 
Put the value of c in the equation (ii), 3a – 2b = 20 ...... (v)
 
By solving equation iv and v we can get the values of a and b and hence we can find their difference as well
 
Therefore, answer can be concluded by combining all the statements.
 
Hence, option D is correct.
5
A dishonest merchant professes to sell his article at Cost price but uses a faulty scale while selling. What is the profit percentage does the merchant make when he sells the article at Cost Price?
 
Statement I : The cost price of the article is Rs. 25 per kg. 
 
Statement II : He uses a scale which weighs less by 20% 
 
Statement III : If he had sold the articles at 20% profit on cost price then his net profit percentage would have been 50%. 
» Explain it
A
From the statement I, we can conclude that the CP = 25 
 
From the statement II, when he sells 100 units that time scale weighs only 80 units 
 
Let the cp of one unit = Rs. 1 then the CP of 80 units = Rs. 80 and the SP of 80 units = Rs. 100 
 
From here we can conclude the profit percentage as 25%. Here we need to calculate percentage value so we don’t have need to exact cost price. 
 
From the statement III, let he sells total 100 units. And the CP of one unit = Rs. 1 
 
Then the SP of 100 units = 120% of 100 = 120 and the net profit percentage = 50% therefore, CP = 80 it means he uses 20% less weight 
 
If he had sold the article at CP then his profit would have been 25% 
 
Hence, option A is correct.