# Data Sufficiency (Quantitative Aptitude)

 1. Find the present age of A.Statement I: Ratio of age of A, B after 5 years is 5:7, and ratio of ages of A, C before 5 years is 5:3. Sum of the age of B after 5 years and C before 5 years is 44 years.Statement II: Ratio of A and C after 7 years is 9:7, Sum of the present age of A and C is 34A. The data given in both statements I and II together are not sufficient to answer the question B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question D. The data given in both statements I and II together are necessary to answer the question E. The data either in statement I alone or in statement II alone is sufficient to answer the questionOption “E” is correct.Answer: EFrom statement I,A’s present age = 5x-5, B’s present age = 7x-5                                 A’s present age = 5y+5 , C’s present age = 3y+55x-5 = 5y+5                            x – y = 27x+3y =44solving this, A’s present age=20From statement II,A’s present age = 9x-7 , C’s present age = 7x-7 9x-7 + 7x-7 = 3416x =48       x=39x-7 = 20                                                   Therefore, either statement I or II is sufficient to answer this question 2. A Bag contains ‘x’ red balls, 7 yellow balls, 8 green balls. Find the total number of balls in the bag.Statement I: If two balls are taken at random, the probability of that balls being red is 1/19Statement II: If two balls are taken at random, the probability of balls being green is 14/95A. The data given in both statements I and II together are not sufficient to answer the question B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question D. The data given in both statements I and II together are necessary to answer the question E. The data either in statement I alone or in statement II alone is sufficient to answer the questionOption “E” is correct.Answer: EFrom statement I,Let no of Red balls = R (Therefore total balls = 15+R)   R=5Total number of balls =20                  Either Statement I or II is sufficient to answer this question. 3. What is the volume of the sphere?Statement I: Radius of the cylinder is equal to the radius of the sphere and the volume of the cylinder is 2772 cm3.Statement II: Volume of the cone is 308 cm3 and the height of the cone is 1 cm less than the radius of the cone and the radius of the cone is equal to the radius of the sphere.A. The data given in both statements I and II together are not sufficient to answer the question B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question D. The data given in both statements I and II together are necessary to answer the question E. The data either in statement I alone or in statement II alone is sufficient to answer the questionOption “B” is correct.Answer: BFrom statement I,Radius of the cylinder is equal to the radius of the sphere and the volume of the cylinder is 2772 cm3.So, Statement I alone is not sufficient to answer the question.From statement II,308 = 1/3 * 22/7 * r * r * (r – 1)294 = r3 – r2r = 7 cmVolume of the sphere = 4/3 * 22/7 * 7 * 7 * 7 = 4312/3 cm3So, Statement II alone is sufficient to answer the question. 4. What is the length of train A?Statement I: Train A crosses train B running in opposite direction in 18 seconds. Train B crosses a 500 m long bridge in 48 seconds and also crosses a man standing in a platform in 18 seconds.Statement II: Train A crosses a platform of length 150 m and train C having length 250 m running in opposite direction in 24 seconds and 21 seconds respectively.A. The data given in both statements I and II together are not sufficient to answer the question B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question D. The data given in both statements I and II together are necessary to answer the question E. The data either in statement I alone or in statement II alone is sufficient to answer the questionOption “D” is correct.Answer: DFrom statement I,Length of train A = xSpeed of train A = ySpeed of train B = zLength of train B = bx + b = (y + z) * 5/18 * 18x + b = 5y + 5zb + 500 = z * 5/18 * 483b + 1500 = 40zb = z * 5/18 * 18b = 5z3b + 1500 = 8bb = 300z = 300/5 = 60So, Statement I alone is not sufficient to answer the question.From statement II,Length of train A = xSpeed of train A = ySpeed of train C = cx + 150 = y * 5/18 * 243x + 450 = 20yx + 250 = (y + c) * 5/18 * 21So, Statement II alone is not sufficient to answer the question. 5. Dinesh and Ramesh entered into a partnership with an investment in the ratio 7 : 5 respectively. After one year, Tanish joined them with investment equal to average of the initial investments of Dinesh and Ramesh. After one more year, Ramesh invested Rs. 20000 more. At the end of three years, they earned a total profit of Rs. 156000. Find the share of Ramesh in the profit.Statement I: Respective ratio of the profit shares of Ramesh and Tanish is 19:12.Statement II: Share of Dinesh in the profit is Rs. 63000.A. The data given in both statements I and II together are not sufficient to answer the question B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question D. The data given in both statements I and II together are necessary to answer the question E. The data either in statement I alone or in statement II alone is sufficient to answer the questionOption “C” is correct.Answer: CLet, initial amounts invested by Dinesh and Ramesh be Rs.7k and Rs.5k respectively.Ratio of shares in the profit:Dinesh : Ramesh : Tanish = (7k x 3) : (5k x 2 + 5k + 20000) : (6k x 2)= 21k : (15k + 20000) : 12k ————— (i)From Statement I:(15k + 20000)/12k = 19/12=> 19k = 15k + 20000=> 19k – 15k = 20000=> 4k = 20000=> k = 20000/4=> k = 5000From (i)Dinesh : Ramesh : Tanish = (21 x 5000) : (15 x 5000 + 20000) : (12 x 5000)= 105000 : 95000 : 60000= 21 : 19 : 12Share of Ramesh in the profit = [19/(21 + 19 + 12)] x 156000= (19/52) x 156000= Rs. 57000From Statement II:[21k/(21k + 15k + 20000 + 12k)] x 156000 = 63000=> 21k/(48k + 20000) x 52 = 21=> 1092k = 1008k + 420000=> 1092k – 1008k = 420000=> 84k = 420000=> k = 420000/84=> k = 5000From (i)Dinesh: Ramesh: Tanish = (21 x 5000): (15 x 5000 + 20000): (12 x 5000)= 105000: 95000: 60000= 21: 19: 12Share of Ramesh in the profit = [19/(21 + 19 +12)] x 156000= (19/52) x 156000= Rs. 57000Hence, data in either in statement I alone or in statement II alone is sufficient to answer the question. 6. Find the difference between compound interest and simple interest on Rs. P at r % per annum after two years.Statement I: Simple interest on Rs. P at r% per annum after five years will be Rs.24000.Statement II: The total amount on compound interest of Rs. 50000 at r% per annum after two years will be Rs. 58320.A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. If the data in either in statement I alone or in statement II alone is sufficient to answer the question. D. If the data in both the statements I and II together are not sufficient to answer the question. E. If the data in both the statements I and II together are necessary to answer the question.Option “E” is correct.Answer: EFrom Statement I:We know thatSI = (P x r x t)/100=> 24000 = (P x r x 5)/100=> P x r = 2400000/5=> P x r = 480000From Statement II:We know thatAmount on CI = P x (1 + r/100)t=>58320 = 50000 x (1 + r/100)2=>58320/50000 = (1 + r/100)2=> 729/625 = (1 + r/100)2=> (27/25)2 = (1 + r/100)2=> 27/25 = 1 + r/100=> 27/25 – 1 = r/100=> (27 – 25)/25 = r/100=> 2 = r/4=> r = 8%From Statement I and II:P x 8 = 480000=> P = Rs. 60000We know that, for two yearsCI – SI = P x (r/100)2= > 60000 x (8/100)2= > 60000 x (8/100) x (8/100)= > Rs. 384Hence, data in both the statements I and II together are necessary to answer the question. 7. Find the share of C?I) A, B and C started a business by investing Rs. 20000, Rs. 30000 and Rs. 40000 respectively. After 7 months, A invested Rs. 10000 more but C withdraw Rs. 10000. The total profit at the end of the year is Rs. 108000II) A and C enter into a partnership by investing Rs. 30000 and Rs. 40000 respectively. After 4 months, B entered into a partnership by investing Rs. 50000.A. Either statement I or statement II is sufficient B. Only statement I is sufficient C. Only statement II is sufficient D. Both the statements I and II together are sufficient E. Neither statement I nor statement II is sufficientOption “B” is correct.Answer: BFrom statement I,The share of A, B and C,= > [20000 * 7 + 30000 * 5]: [30000 * 12]: [40000 * 7 + 30000 * 5]= > [140000 + 150000]: : [280000 + 150000]= > 290000: 360000: 430000= > 29: 36: 43108’s = 1080001’s = 1000The share of C = 43’s = Rs. 43000Only statement I alone is sufficient to answer the question. 8. How long will 15 women and 6 men take to do the work?I) 6 women and 8 men can do a work in 4 days.II) 9 women and 10 men can do the same work in 3 days.A. Either statement I or statement II is sufficient B. Only statement I is sufficient C. Only statement II is sufficient D. Both the statements I and II together are sufficient E. Neither statement I nor statement II is sufficientOption “D” is correct.Answer: DFrom statement I,6 women and 8 men can do a work in 4 daysThis statement alone is not sufficient to answer the question. From statement II,9 women and 10 men can do the same work in 3 daysThis statement alone is not sufficient to answer the question. From statement I and II,Total work = (men (or) women) * daysWork equal. So,(6w + 8m) * 4 = (9w + 10m) * 324w + 32m = 27w + 30m2m = 3w15w + 6m = 10m + 6m = 16 m6w + 8m = 4m + 8m = 12 mMen   days12      416      ?(12 * 4) = (16 * x)x = 3 daysBoth the Statement I and II are sufficient to answer the question. 9. Find the age of Neelima after six years.Statement I: Average of the present ages of Neelima, Sekhar and Sikha is 20 years. Respective ratio of the ages of Sekhar and Sikha before five years was 3:4.Statement II: Respective ratio of the ages of Sekhar and Sikha after five years will be 5:6.A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. If the data in either in statement I alone or in statement II alone is sufficient to answer the question D. If the data in both the statements I and II together are not sufficient to answer the question E. If the data in both the statements I and II together are necessary to answer the question.Option “E” is correct.Answer: EFrom Statement I:Neelima + Sekhar + Sikha = 3 x 20 = 60Respective ratio of the ages of Sekhar and Sikha before five years was 3:4.From Statement II:Respective ratio of the ages of Sekhar and Sikha after five years will be 5:6.From Statement I and II:Let, ages of Sekhar and Sikha before five years be 3k years and 4k years respectively.(3k + 10)/(4k + 10) = 5/6=> 18k + 60 = 20k + 50=> 20k – 18k = 60 – 50=> 2k = 10=> k = 5Present age of Sekhar = 3k + 5 = 3 x 5 + 5 = 20 yearsPresent age of Sikha = 4k + 5 = 4 x 5 + 5 = 25 yearsNeelima + Sekhar + Sikha = 3 x 20 = 60=>Neelima + 20 + 25 = 60=>Neelima = 60 – 45=>Neelima = 15Age of Neelima after six years = 15 + 6 = 21 yearsHence, data in both the statements I and II together are necessary to answer the question. 10. The number of employees in company A is 5400. What is the ratio of the number of male employees in B to the number of female employees in B?Statement I: The number of male employees in B is 11% more than the number of male employees in A and the number of female employees in B is 17% more than the number of female employees in B.Statement II: The number of female employees in B is 612 more than the total number of female employees in A.A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C. If the data in either in statement I alone or in statement II alone is sufficient to answer the question D. If the data in both the statements I and II together are not sufficient to answer the question E. If the data in both the statements I and II together are necessary to answer the question.Option “E” is correct.Answer: EFrom statement I,Number of employees in A = 5400Number of female employees in A = xNumber of male employees in A = yNumber of male employees in B = y * 111/100Number of female employees in B = x * 117/100So, Statement I alone is not sufficient to answer the question.From statement II,Number of female employees in B – number of female employees in A = 612So, Statement II alone is not sufficient to answer the question.From statement I and II,117x/100 – x = 61217x = 61200x = 3600Number of male employees in A = 5400 – 3600 = 1800Required ratio = 1800 * 111/100: 3600 * 117/100= 37: 78Both statements are necessary to answer the question.
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