Question – 1
1. What least number should be subtracted from 2590 so that the remainder when divided by 9, 11 and 13 will leave in each case the same emainder 6? Which of the following statements is true? Indicate the corrrect option.
- A. 2
- B. 3
- C. 6
- D. 10
- E. 14
- Answer:D
- Answer Explanation:The remainder will be divisible by the LCM of 9, 11 and 13LCM = 12871287*2=25742574+6=25802590-2580=10Hence, the required number is 10.
Question – 2
2. Which is the smallest number by which 19404 should be multiplied to make it a perfect square? Indicate the correct option.
- A. 2
- B. 3
- C. 7
- D. 11
- E. 22
- Answer:D
- Answer Explanation:19404=2*2*3*3*7*7*1119404 should be multiplied by 11 to make it a perfect square.Option D is true..
Question – 3
3. If a/b = 1/5 which of the following is equal to (3a+2b)/(3a-2b)? Indicate the correct option.
- A. 13/5
- B. 91/25
- C. -91/25
- D. -13/7
- E. 7/5
- Answer:D
- Answer Explanation:(3a+2b)/(3a-2b) = (3a/b+2)/(3a/b-2)= (3*1/5+2)/(3*1/5-2)= (3/5+2)/(3/5-2)= (3+10)/5/(3-10)/5= 13/-7=-13/7Option D is true.
Question – 4
4. Find the next number in the series 12, 17, 23, 30, 38. Indicate the correct option.
- A. 48
- B. 43
- C. 47
- D. 51
- E. 45
- Answer:C
- Answer Explanation:17-12=523-17=630-23=738-30=8Hence, consecutive numbers are added in the series.The next number will be 38+9=47Option C is correct.
Question – 5
5. The price of commodity A is $5800 and it decreases at the rate of $2 per three months. Commodity B costs $4200 and it increases at the rate of $8 per four months. How many years will it take for the two commodities to become equal in price? Indicate the correct option.
- A. 4.5
- B. 3.8
- C. 20
- D. 60
- E. 50
- Answer:E
- Answer Explanation:Price reduction of A in one year = 4*2 = 8Price increase of B after one year = 3*8 = 24Let the prices of the two commodities be the same after x years5800-8x=4200+24×5800-4200=24x+8×1600=32xx=50Hence, it shall take 50 years.Option E is correct.
Question – 6
(Note: [x^2=x*x] )
- A. a^2/4c
- B. -a^2/4c
- C. -a/2c
- D. a/2c
- E. c^2/4a
- Answer:E
- Answer Explanation:For the roots to be equal, the discriminant has to be zero.c^2-4*a*b=0c^2=4abb=c^2/4aOption E is correct.
Question – 7
7. Alice can knit a sweater in 30 days, Laura in 20 days and Sandra in 60 days. How many days will they take to knit the sweater if they share their work? Indicate the correct option.
- A. 5
- B. 10
- C. 15
- D. 20
- E. 25
- Answer:B
- Answer Explanation:Work done by Alice in one day = 1/30Work done by Laura in one day = 1/20Work done by Sandra in one day = 1/60Work done by them working together in one day = 1/20+1/30+1/60= (3+2+1)/60= 6/60=1/10Time taken to compete the work = 10 daysOption B is correct.
Question – 8
8. A boat takes 6 hours to go downstream and upstream a certain distance. It takes 4 hours to travel twice the distance downstream. Which of the following is the ratio of the speed of the boat in still water to the speed of the river? Indicate the correct option.
- A. 3:1
- B. 1:3
- C. 5:3
- D. 3:5
- E. 7:9
- Answer:A
- Answer Explanation:Let the speed of the boat in still water be x and the speed of the river be ySpeed upstream = x-ySpeed downstream = x+yLet the distance travelled be DTime = Distance/SpeedD/(x+y) + D/(x-y) = 6 and 2D/(x+y) = 4Putting D/(x+y)=2 …(1) in the first relation, we get2 + D/(x-y) = 6D/(x-y) = 4 …(2)From (1) and (2), we get(x+y)/(x-y) = 4/2 = 2x+y=2x-2yx-2x=-2y-y-x=-3yx/y = 3/1Option A is true.
Question – 9
9. Which of the following is equal to 2% of 22% of 222? Indicate the correct option.
- A. 97.68
- B. 0.2442
- C. 24.42
- D. 48.84
- E. 0.9768
- Answer:E
- Answer Explanation:2% of 22% of 222 = 2% of 22*222/100= 2% of 48.84= 0.9768Option E is correct.
Question – 10
10. Which of the following is the average of the first 10 even numbers? Indicate the correct option.
- A. 20
- B. 15
- C. 10
- D. 5
- E. 18
- Answer:C
- Answer Explanation:The numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20Average = (2+4+6+8+10+12+14+16+18+20)/10= 10
Question – 11
11. By what number should each of 15, 24, 51 and 87 be lessened so that the remainders are in proportion? Indicate the correct option.
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
- Answer:C
- Answer Explanation:Let the number be x15-x:24-x=51-x:87-x(15-x)(87-x) = (24-x)(51-x)1305-15x-87x+x^2=1224-51x-24x+x^21305-1224=-75x+102×81=27xx=3The number is 3[x^2=x*x].
Question – 12
12. Sam lent $4000 to Pam for two years at 5% simple interest. After two years, he lent the complete amount to Ann for three years at 7%. What was the interest returned by Ann? Indicate the correct option.
- A. $4924
- B. $924
- C. $400
- D. $1324
- E. $5324
- Answer:B
- Answer Explanation:Simple interest SI is given by SI =P*R*T/100, where P, R and T are principle, rate and time.Amount returned by Pam = 4000+ SI= 4000 + 4000*5*2/100= 4000 + 400= 4400Interest returned by Ann after three years = 4400*7*3/100= 924Option B is correct.
Question – 13
13. How many terms are required at the least to add up to at least 100 in the series 3, 5, 7, 9 …? Indicate the correct value.
- A. 16
- B. 33
- C. 15
- D. 10
- E. 35
- Answer:D
- Answer Explanation:The series is an AP with the first term a = 3 and common difference 5-3=2Let n terms as up to at least 100Sum of n terms Sn = n/2[2a+(n-1)d]100<=n/2[2*3+(n-1)*2]100<=n/2[6+2n-2]100<=n/2[4+2n]100<=n(2+n)n=10At least 10 terms add up to at least 100 in the given series.
Question – 14
14. Annie and Simmi run a race of 2km. Annie beats Simmi by 30m. Simmi reaches the finish line 6 seconds after Annie does. How long did Annie take to complete the distance? Indicate the correct option.
- A. 9004 seconds
- B. 1900 seconds
- C. 19994 seconds
- D. 9994 seconds
- E. 9546 seconds
- Answer:D
- Answer Explanation:Time taken by Simmi to cover 30 m = 6 secSpeed of Simmi in m/s=30/6 = 5m/sTime taken by Simmi to cover 2 km = Distance*speed= 2000*5 = 10000 secTime taken by Annie to cover 2 km = 10000 – 6 seconds = 9994 secondsOption D is correct.
Question – 15
15. A dishonest shopkeeper mixes water in acid to earn a profit. He sells acid worth $5.4/litre at $4.2/litre. If he initially had 14 litres of acid then how many litres of water did he add to it? Indicate the correct option.
- A. 1l
- B. 2l
- C. 3l
- D. 4l
- E. 5l
- Answer:D
- Answer Explanation:Let the quantity of water added be x litre.Total quantity = (14+x) litreAs per the conditions, we have(14+x)*4.2=14*5.458.8+4.2x=75.64.2x=75.6-58.84.2x=16.8x=4Option D is correct.