The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
A) The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B) The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C) The data either in statement I alone or in statement II alone are sufficient to answer the question.
D) The data given in both statements I and II together are not sufficient to answer the question.
E) The data in both statements I and II together are necessary to answer the question
"Consider the five-digit number 15xy6, where 'x' and 'y' are digits. Find the sum 'x + y.'
Statement I: 15xy6 is divisible by 79.
Statement II: The product of 'x' and 'y' is a multiple of 16, and 'xy' is a two-digit number less than 80."
Now, you need to assess whether each statement, independently or together, provides enough information to determine 'x + y.'
ATQ, Statement I: The number can be: Only 15326 is divisible by 79 So, x + y = 3 + 2 = 5 So, data in statement I alone is sufficient to answer the question. Statement II: Since xy is a multiple of 16 and less than 80, so ‘xy’ can be 16, 32, 48, and 64. So, data in statement II alone is not sufficient to answer the question.
"There is a mixture of soda and lime in the ratio of 9:7. We want to determine the quantity of the original mixture.
Statement I: If we remove 192 ml of the mixture and then add 'x + 18' ml of soda and 'x + 4' ml of lime into the remaining mixture, the quantity of lime in the resultant mixture will be 25% less than the quantity of soda.
Statement II: If we remove 240 ml of the mixture and then add 'y + 15' ml of soda and 'y - 55' ml of lime into the remaining mixture, the quantity of soda in the resultant mixture becomes 60%.
Statement III: If we remove 320 ml of the mixture and then add 'z + 25' ml of soda and 'z + 45' ml of lime into the remaining mixture, the quantity of soda in the resultant mixture becomes 50%."
Now, you need to determine if each statement, individually or in combination, provides enough information to calculate the quantity of the original mixture.
ATQ, Let, quantity of Soda and Lime in the original mixture is ‘9a’ ml and ‘7a’ ml respectively. Statement I: Quantity of soda in 192 ml of mixture = 9/16 × 192 = 108 ml Quantity of Lime in 192 ml of mixture = 192 – 108 = 84 ml According to statement; 0.75 × (9a – 108 + x + 18) = 7a – 84 + x + 4 Or, 6.75a – 67.5 + 0.75x = 7a + x – 80 Or, 0.25a + 0.25x = 12.5 Or, a + x = 50 Since, we cannot find the value of ‘a’ and ‘x’. So, data in statement I alone is not sufficient to answer the question. Statement II: Quantity of soda in 240 ml of mixture = 9/16 × 240 = 135 ml Quantity of lime in 240 ml of mixture = 240 – 135 = 105 ml According to statement; 9a – 135 + y + 15 = 0.60 × (9a + 7a + y + 15 + y – 55 – 240) Or, 9a + y – 120 = 9.6a + 1.2y – 168 Or, 0.6a + 0.2a = 48 Since, we cannot find the value of ‘a’ and ‘y’. So, data in statement II alone is not sufficient to answer the question. Statement III: Quantity of soda in 320 ml of mixture = 9/16 × 320 = 180 ml Quantity of lime in 320 ml of mixture = 320 – 180 = 140 ml According to statement; 9a – 180 + z + 25 = 7a – 140 + z + 45 Or, 2a = 60 Or, a = 30 Total quantity of original mixture = 16a = 16 × 30 = 480 ml So, data in statement III alone is sufficient to answer the question.
Arunima covered ‘a’ km, partly by Cycle, partly by Bike and rest by Walking. Find the speed of the Cycle.
Statement I: The man covered the total distance in 12 hours such that he covers 200 km by Cycle, 300 km by Bike and 360 km by Walking.
Statement II: The ratio of speeds of the Cycle, Bike and by Walking is 1:3:2, respectively.
Statement III: The difference between the speeds of the Cycle and by Walking is 40 km/hr.
Statement I: Arunima covered the total distance in 12 hours such that he covers 200 km by Cycle, 300 km by bike and 360 km by walking. So, data in statement I alone is not sufficient to answer the question. Statement II: Let the speed of the Cycle, the bike and the walking be ‘y’ km/hr, 3y km/hr and 2y km/hr, respectively So, data in statement II alone is not sufficient to answer the question. Statement III: The difference between the speeds of the Cycle and the walking is 40 km/hr. Combining statements I and II: (200/y) + (300/3y) + (360/2y) = 12 Or, 480 = 12y Or, y = 40 Therefore, speed of the Cycle = 40 km/hr So, data in statement I and II together is sufficient to answer the question. Combining statement II and III: 2y – y = 40 Or, y = 40 Therefore, speed of the Cycle = y = 40 km/hr So, data in statement II and III together is sufficient to answer the question. Combining statement I and III: We cannot determine the speed of the Cycle. So, data either in statement I and II or in statement II and III are sufficient to answer the question while data in statement I and III together are not sufficient to answer the question.
We have two vessels, A and B, each containing a mixture of milk and Bournvita. The ratios of milk to Bournvita in these vessels are 9:7 and 13:12, respectively. We want to find the difference between the quantities of the mixture in Vessel A and Vessel B.
Statement I: The amount of milk in Vessel A is 34 liters more than the amount of milk in Vessel B, and the combined quantity of Bournvita in both mixtures is 336 liters.
Statement II: The quantity of Bournvita in both Vessels is the same, and the total amount of milk in both Vessels is 398 liters.
Now, you need to determine if each statement, separately or in combination, provides enough information to calculate the difference between the quantities of the mixture in Vessels A and B.
ATQ, Let, quantity of milk and Bournvita in mixture A is 9x litres and 7x litres, respectively. Let, quantity of milk and Bournvita in mixture B is 13y litres and 12y litres, respectively. Statement I: 9x – 13y = 34………………..(1) And, 7x + 12y = 336………………(2) Solving equation (1) and (2), we get x = 24 and y = 14 Desired difference = 16 × 24 – 25 × 14 = 384 – 350 = 34 litres So, data in statement I alone is sufficient to answer the question. Statement II: 7x = 12y x = 12y/7 And, 9x + 13y = 398 Or, 108y/7 + 13y = 398 Or, 199y/7 = 398 y = 14 x = 14 × 12/7 = 24 Desired difference = 16 × 24 – 25 × 14 = 384 – 350 = 34 litres So, data in statement II alone is sufficient to answer the question.
Virat invested Rs. (X + Y) in SIP A and Rs. (X - Y) in SIP B. We want to determine the ratio of the total amount invested in SIP A to that in SIP B, where SIP A offers a 15% annual simple interest, and SIP B offers a 20% annual compound interest, compounded annually.
Statement I: The difference between the amounts invested in both SIPs is Rs. 2400, and the interest received from SIP B after 3 years is Rs. 436.8.
Statement II: The total amount invested in both SIPs is Rs. 3600, and the interest received from SIP A at the end of 6 years is Rs. 2700.
Statement III: The interest received from SIP B is 70(2/3)% less than the interest received from SIP A after 2 years."
Now, you need to determine if each statement, individually or together, provides enough information to calculate the ratio of the total investments in SIP A and SIP B.
ATQ, Statement I: (X + Y) – (X – Y) = 2400 2X = 2400 X = 1200 Since, interest received from SIP B after 3 years is Rs. 436.8. So, (Y – X) × [(1.2) 3 – 1] = 436.8 (Y – X) = 436.8/0.728 = 600 Y = X + 600 = 1800 Amount invested in SIP A = 1800 + 1200 = Rs. 3000 Amount invested in SIP B = 1800 – 1200 = Rs. 600 Desired Ratio = 3000:600 = 5:1 So, statement I alone is sufficient to answer the question. Statement II: (Y – X) + (X + Y) = 3600 2Y = 3600 Y = 1800 And, (X + Y) × 0.15 × 6 = 2700 X + Y = 2700/0.90 = 3000 X = 3000 – 1800 = 1200 Amount invested in SIP A = 1800 + 1200 = Rs. 3000 Amount invested in SIP B = 1800 – 1200 = Rs. 600 Desired Ratio = 3000:600 = 5:1 So, statement II alone is sufficient to answer the question. Statement III: Interest received from SIP A after 2 years = (X + Y) × 0.15 × 2 = Rs. 0.3(X + Y) Interest received from SIP B after 2 years = [(1.2)2 – 1] × (Y – X) = Rs. {0.44 × (Y – X)} According to question, 0.44 × (Y – X) = 29(1/3)% of 0.3(X + Y) 0.44 × (Q – P) = 88/3 × 1/100 × 0.3(X + Y) (X + Y)/(Y – X) = 0.44/0.088 = 5 Desired ratio = 5:1 So, statement III alone is sufficient to answer the question.
If a train takes 8 seconds to cross a pole and 19.2 seconds to cross platform 'A', then find the time taken by the train to cross a 105-metres long platform.
Statement I: The lengths of the train and platform 'A' are in ratio 5:7, respectively.
Statement II: Difference between length of the train and platform 'A' is 25 metres.
Statement III : The train takes 24 seconds to cross a bridge that is 37.5 metres longer than platform 'A'.
Let the speed of the train be 's' m/s Length of the train = 8 × s = '8s' metres Length of train + Length of platform 'A' = 19.2 × s = 19.2s metres Or, Length of platform = 19.2s - 8s = 11.2s metres Statement I: Length of platform = (7/5) × 8s = '11.2s' Since, we cannot find the value of 's'. So, data in statement I alone is not sufficient to answer the question. Statement II: 11.2s - 8s = 25 Or, s = (125/16) So, length of train = 8 × (125/16) = 62.5 metres Required time = {(105 + 62.5)/(125/16)} = 21.44 seconds So, data in statement II alone is sufficient to answer the question. Statement III: Length of bridge = (11.2s + 37.5) metres So, [{11.2s + 37.5 + 8s}/s] = 24 Or, 4.8s = 37.5 Or, s = (125/16) Required time = {(105 + 62.5)/(125/16)} = 21.44 seconds So, data in statement III alone is sufficient to answer the question So, data given in either statement II alone or in statement III alone are sufficient to answer the question while the data given in statement I alone is not sufficient to answer the question
The cost price of articles 'A' and 'B' are in ratio 5:6, respectively. The amount of discount allowed on article 'A' and 'B' were in ratio 4:3, respectively, then the profit earned on selling both articles would be same. Find the selling price of article 'A'.
Statement I: Marked price of both articles is Rs. 500, each.
Statement II: If the amount of discount allowed on article 'A' to 'B' were in ratio of 3:4 while keeping the amount of total discount given being same, then the profit earned on selling article 'A' would've been of Rs. 100.
Statement III: If the seller offers a discount of 40% on its marked price, then there is no loss but as soon as the discount is more than 40%, there is loss.
Let the cost price of article 'A' and 'B' be Rs. '5x' and Rs. '6x', respectively. Let the discount allowed on selling article 'A' and 'B' be Rs. '4y' and Rs. '3y', respectively. Statement I: According to statement; 500 - 4y - 5x = 500- 3y - 6x Or, x = y So, data in statement I alone is not sufficient to answer the question. Statement II: Let the marked price of the article be Rs. 'M'. So, M - 3y = 5x + 100 So, data in statement II alone is not sufficient to answer the question. Statement III: Since, a discount of 40% on the article is break-even point (no profit no loss) Let marked price of the article 'B' is Rs. 'M' So, 0.6 × M = 6x Or, M = 10x So, data in statement III alone is not sufficient to answer the question. On, combining statement 'I' and 'II' we have; 500 - 3y = 5x + 100 Or, 400 = 5x + 3y Or, 400 = 5x + 3x (Since, x = y) Or, 400 = 8x So, x = 50 So, y = 50 So, selling price of article 'A' = 50 × 10 - 4 × 50 = Rs. 300 So, data given in statement 'I' and 'II' combined is sufficient to answer the question. On, combining statement 'I' and 'III' we have; Marked price of the article = 500 And, M = 10x So, 500 = 10x => x = 50 y = 50 Selling price of article A = 50 × 10 - 4 × 50 = Rs. 300 so, The data given either in statement I and II together or in statement I and III together is sufficient to answer the question.
