mathewhe/aqua_rat huggingface dataset:
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 1976 sq m
(B) 2176 sq m
(C) 4312 sq m
(D) 1269 sq m
(E) 2679 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:C
Answer: (C) 4312 sq m
Question: If 4 men can colour 48 m long cloth in 2 days, then 2 men can colour 36 m long cloth in
(A) 1 day
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 2 = 3 day.
C
Answer: (C) 3 days
Question: A sum of Rs.4700 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) Rs.2520
(B) Rs.3055
(C) Rs.3320
(D) Rs.2760
(E) None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4700[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4700 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7755
So the interest = 7755 - 4700 = Rs.3055
ANSWER:B
Answer: (B) Rs.3055
Question: A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed afurther 10% reduction on thedis counted price. If a staff member buys thedress what will she have to pay in terms of X?
(A) 0.560X
(B) 0.560X
(C) 0.765X
(D) 0.608X
(E) 0.895X
Rationale: If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X
C
Answer: (C) 0.765X
Question: Cost of 2 bats and 3 balls is Rs.1300. The cost of 3 bats and 2 balls is Rs.1200. The cost of each balls is more than that of each bat by?
(A) 50
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: 2Bats + 3Ball = 1300 --- (1)
3Bats + 3Ball = 1200 --- (2)
Subtracting 2nd from 1st, we get
-Bats + Ball = 100 => Ball - Bats = 100
B
Answer: (B) 100
Question: If 11 and 13 are prime numbers, which of the following CANNOT be the sum of a and b?
(A) 24
(B) 48
(C) 72
(D) 47
(E) 96
Rationale: ans =D
Answer: (D) 47
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
(A) 3 : 5 : 2
(B) 3 : 5 : 5
(C) 6 : 10 : 5
(D) 8 : 12 : 4
(E) Data inadequate
Rationale: Explanation:
Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer is C
Answer: (C) 6 : 10 : 5
Question: A shop keeper had some books. He sells 40% books and still has 420 books. Originally, he had
(A) 588 books
(B) 600 books
(C) 620 books
(D) 700 books
(E) None of these
Rationale: Explanation :
Suppose originally he had x books.
Then,(100-40)% of x = 420.
=>60/100x = 420
=>x = (420 100 / 60
=>x=700.
Answer : D
Answer: (D) 700 books
Question: There were totally 100 men.81 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 100-(100-81)-(100-75)-(100-85)-(100-70)= 100-19-25-15-30=100-89=11
ANSWER:A
Answer: (A) 11
Question: When 200 is divided by positive integer x, the remainder is 5. What is the remainder when 395 is divided by x?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 5
Rationale: if 200/x leaves a reminder 5 then (200-5) i.e. 195 is divisible by x
So (200+195)/x leaves a reminder rem(200/x)+rem(195/x)=> 5+0=5
Answer :E
Answer: (E) 5
Question: A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 17}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
(A) 15
(B) 16
(C) 19
(D) 20
(E) 36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 20
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
D
Answer: (D) 20
Question: A 270m long train running at the speed of 120kmph crosses another train running in opposite direction at the speed of 80kmph in 9 second. What is the length of the other train?
(A) 150m
(B) 230m
(C) 290m
(D) 310m
(E) 420m
Rationale: Relative speed = 120+80 = 200*5/18 = 500/9 m/s
Let the length of the other train be x meters
x+270/9 = 500/9
x = 230m
Answer is B
Answer: (B) 230m
Question: A sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest. What is the rate of interest?
(A) 2%
(B) 1%
(C) 7%
(D) 5%
(E) 8%
Rationale: C
7%
S.I. = (21200 - 15600) = 5600.
Rate = (100 x 5600)/(15600x5)% = 7%
Answer: (C) 7%
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/6
(E) 1/3
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: (C) 1/5
Question: (540 + ?) × 3/5 - 120 = 483
(A) A)465
(B) B)450
(C) C)540
(D) D)20
(E) E)120
Rationale: Explanation:
=> (540 + ?) × 3/5 - 120 = 483
=> (540 + ?) × 3/5 = 483 + 120
=> (540 + ?) × 3/5 = 603
=> ? = 603 × 5/3 - 540 = 1005 - 540 = 465
Answer: Option A
Answer: (A) A)465
Question: Lilly has 10 fish and Rosy has 14 fish. In total, how many fish do they have in all?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: 10+14=24
The answer is D.
Answer: (D) 24
Question: What quantity of water should be added to reduce 20 liters of 80% acidic liquid to 20% acidic liquid?
(A) 30liters
(B) 50liters
(C) 60liters
(D) 70liters
(E) 80liters
Rationale: Acid in 20 liters = 80% of 20 = 16 liters
Suppose x liters of water be added.
Then 16 liters of acid in 20+x liters of diluted solution
20% of 20+x = 16
20+x = 80
x = 60liters
Answer is C
Answer: (C) 60liters
Question: Ashis's height is 25% more than Babji, by how much percent Babji's height is less than Ashis.
(A) 30%
(B) 25%
(C) 75%
(D) 20%
(E) None of these
Rationale: Explanation :
Solution: Babji is less than Ashis by (25/(100+25) * 100)% = 20%
Answer : D
Answer: (D) 20%
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 210 m long?
(A) 34 Seconds
(B) 22 Seconds
(C) 21 Seconds
(D) 24 Seconds
(E) 29 Seconds
Rationale: Distance travelled = 140 + 210m = 350m
Speed = 60 * 5/8 = 50/3m
Time = 350 * 3/50 = 21 Seconds
ANSWER C
Answer: (C) 21 Seconds
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 35 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
(A) 80 lakh
(B) 56 lakh
(C) 40 lakh
(D) 60 lakh
(E) None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+35/8x=5/4 ⇒ 20x + 140 = 40x
∴ x = 7
∴ Income of company B = 8x = 56 lakh
Answer B
Answer: (B) 56 lakh
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.250
(B) Rs.300
(C) Rs.320
(D) Rs.340
(E) Rs.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
A
Answer: (A) Rs.250
Question: If N is the least positive integer that is divisible by every integer from 3 to 10 inclusive, then N/7 is =
(A)  360
(B)  720
(C)  2520
(D)  3960
(E)  6720
Rationale: The integer should be divisible by: 3, 4, 5, 6, 7, 8, 9 and 10, that is 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, N/7 is (7 * 5 * 3^2 * 2^3)/7 = 5*9*8 = 360.
Answer: A.
Answer: (A)  360
Question: If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark?
(A) A)60%
(B) B)85.7%
(C) C)65%
(D) D)75%
(E) of these
Rationale: A's marks = 70 ; B's marks = 60.
Let x% of A = B => x/100 *70 = 60
=> x = (60 * 100)/80 = 85.7
B's marks is 85.7% of A's marks.
ANSWER:B
Answer: (B) B)85.7%
Question: A male leader is to be selected from a class of students having 15 boys and 20 girls. In how many ways can select?
(A) 50 ways
(B) 7/3 ways
(C) 3/7 ways
(D) 35 ways
(E) 15 ways
Rationale: The number of boy student in the class is 15. Therefore required number of selection =15. Answer : E
Answer: (E) 15 ways
Question: How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
(A) 42
(B) 50
(C) 30
(D) 28
(E) 26
Rationale: Explanation:
Distance = 500m
Speed = 63 -3 km/hr = 60 km/hr = 600/36 m/s = 50/3 m/s
Time taken = distance/speed = 500/(50/3) = 30 s
Answer: Option C
Answer: (C) 30
Question: Kid have 8 black balls and 8 white balls. He is trying to arrange a ball in a row then in how many ways can he arrange these balls in a row so that balls of different colors alternate?
(A) 3×(4!)^2
(B) 1×(9!)^3
(C) 2×(8!)^2
(D) 2×(8!)
(E) 2×6^2
Rationale: 8 black balls can be arranged in 8! ways ...(A)
Now we need to arrange white balls such that white balls and black balls are positioned alternatively. i.e., we can arrange 8 white balls either in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I as shown below.
8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H in 8! ways.
8 white balls can be arranged in the 8 positions marked as B,C,D,E,F,G,H,I in 8! ways.
8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I in 8!+8!=2×8! ways ...(B)
From (A) and (B),
required number of ways =8!×2×8!=2×(8!)^2
C
Answer: (C) 2×(8!)^2
Question: If √x = x, then which of the following must be true?
(A) x is positive
(B) x=1
(C) x^2>x
(D) x is non-negative
(E) None of the above
Rationale: Square both the sides we get
x = x^2
x^2 - x= 0
x(x-1)=0
either x=0 or x=1
So, answer will be D
Answer: (D) x is non-negative
Question: Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $600. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
(A) 11%
(B) 25%
(C) 44%
(D) 50%
(E) 125%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 600
Saving in 2nd year + 240 = 600
Saving in 2nd year = 600 - 240 = 360
Change in Value = 360 - 240 = 120
Original Value = 240
Percentage Increase = (120 / 240 ) * 100
= (1/2 ) * 100 = 50 % ..... Answer D......
Answer: (D) 50%
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Given that A+B = 12 + B + C
=> A – C = 12 + B – B = 12
=> C is younger than A by 12 years
Answer: Option B
Answer: (B) 12
Question: In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s $20,000 annual budget is dedicated to clothes and shoes?
(A) $1,500
(B) $3,000
(C) $4,500
(D) $5,000
(E) $5,400
Rationale: Given for clothes and shoes” takes up 54° of the circular chart.
Then clothes and shoes = 54/360 * 20000.
=> 3000.
Answer:option B is correct answer...
Answer: (B) $3,000
Question: In an automobile market of spare parts dealers and workshops, average earning of a spare parts dealer per day is $520 and the average earning of a workshop is $700. Considering there are 40 shops in market and number of spare parts dealer shops exceeds the workshops by 4. What is the average earning of this market consisting of only spare parts dealers and workshops.
(A) 535
(B) 562
(C) 594
(D) 601
(E) 648
Rationale: Let the number of workshops be x
number of s.p.d=x+4
x+x+4=40 = 2x=36 = x=18
workshops are 18 in number and spd are 22 in number
Average earning of the market= ((520x22)+(700x18))/40
=(11440+12600)/40
=24040/40
=601
Answer: D
Answer: (D) 601
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
(A) 51.25
(B) 51.29
(C) 51.22
(D) 51.38
(E) 51.12
Rationale: Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500)
= Rs.51.25.
Answer: a
Answer: (A) 51.25
Question: Each cell of a certain kind of bacteria produces two more cells. The life span of each cell is 10 minutes and each cell multiples only once in its life time, when it is exactly one minute old. If a new cell is placed in an empty box at time t = 0, then how many live cells will be there in the box just after t = 20 minutes?
(A) 2048 × 1023
(B) 1024 × 1023 cells
(C) (1024)²
(D) 1023 × 1025
(E) 1023 × 1026
Rationale: see total cells created after
1min be 2^1
2min be 2^2
3 min be 2^3.......
thus after 20 min 2^20 will be created
now after 10 min 1 cell will die (2^0)
after 11 min 2 cells die (2^1)
similarly after 20 min 2^10 cells die
thus total cells remained=(2^20)-(1024)
or (1024)^2-1024
or1024*(1024-1)
i.e, 1024*1023
ANSWER:B
Answer: (B) 1024 × 1023 cells
Question: A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 60 vehicles that are not Speedsters, how many Speedster convertibles are there?
(A) 36
(B) 96
(C) 100
(D) 76
(E) 72
Rationale: Total Vehicle = 2/3 of speedster + 1/3 of others.
Speedster convertibles = 2/3 total vehicle * 4 /5
Given : 1/3 constitutes 60 Vehicles. hence 2/3 constitutes 120
Speedster convertibls = 120 * 4/5 = 96
B
Answer: (B) 96
Question: The difference between the place values of two sevens in the numeral 69758472 is
(A) 0
(B) 100
(C) 6993
(D) 699930
(E) None of these
Rationale: Required difference = (700000 - 70) = 699930
Answer: Option D
Answer: (D) 699930
Question: Average expenditure of a person for the first 3 days of a week is Rs. 310 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
(A) 350
(B) 370
(C) 390
(D) 430
(E) None
Rationale: Explanation:
Assumed mean = Rs. 310
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 310 + Rs. 40 = Rs. 350
Correct Option: A
Answer: (A) 350
Question: Tom planted vegetables in a rectangular garden that was 25 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
(A) 175 sq. ft.
(B) 176 sq. ft.
(C) 177 sq. ft.
(D) 178 sq. ft.
(E) 179 sq. ft.
Rationale: area of garden is 25 x 15 = 375 sq. ft.
1/3 x 375 = 125 sq. ft. for corn
1/5 x 375 = 75 sq. ft. for peas
125 + 75 = 200 sq. ft. used
375 - 200 = 175 sq. ft. left over
correct answer A
Answer: (A) 175 sq. ft.
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first flip but not on the last 4 flips?
(A) 1/4
(B) 1/8
(C) 1/16
(D) 1/32
(E) 1/64
Rationale: P(HTTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
The answer is D.
Answer: (D) 1/32
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
(A) 12 : 15 :19
(B) 12 : 15 :29
(C) 12 : 15 :11
(D) 12 : 15 :16
(E) 12 : 15 :13
Rationale: Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24)
= 12 : 15 : 16.
Answer: D
Answer: (D) 12 : 15 :16
Question: Bank account A contains exactly x dollars, an amount that will decrease by 10% each month for the next two months. Bank account B contains exactly y dollars, an amount that will increase by 20% each month for the next two months. If A and B contain the same amount at the end of two months, what is the ratio of x√x to y√y?
(A) 4 : 3
(B) 3 : 2
(C) 16 : 9
(D) 2 : 1
(E) 9 : 4
Rationale: Explanation:
Account A has amount after 2 months = 0.9*0.9*x = 0.81*x
Account B has amount after 2 months = 1.2*1.2*y = 1.44*y
0.81*x=1.44*y --> √(x/y)=√(1.44/0.81) = 12/9 = 4/3.
Ans A
Answer: (A) 4 : 3
Question: |x+3| – |4-x| = |5+x| How many solutions will this equation have?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, so it becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) = 4
E
Answer: (E) 4
Question: At a certain school 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?
(A) 1) 3/4
(B) 2)1/5
(C) 3)2/5
(D) 4)1/2
(E) 5)4/5
Rationale: This is the way to approach the question:
25% of the students join a band => 25% of the students either only join a band or both join a band and play sports
25% of the students play sports => 25% of the students either only play sports or both play sports and join a band
If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both
=20%/25% = 4/5
The answer is therefore (E)
Answer: (E) 5)4/5
Question: What is the units digit of 18! + 1 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.
The units digit of 18! + 1 is 1.
The answer is A.
Answer: (A) 1
Question: A 14 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
(A) 5/14
(B) 3/14
(C) 8/21
(D) 6/7
(E) 2/5
Rationale: A square with an area of 4 has a perimeter of 8.
For the area to be >4, the longer piece must be >8.
The wire must be cut within 6 meters from either end.
The probability of this is 12/14 = 6/7.
The answer is D.
Answer: (D) 6/7
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.50 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 12
(B) 77
(C) 66
(D) 99
(E) 11
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.50 + 1.25 = 2.75 km = 2750 m.
Required time = 2750 * 3/125 = 66 sec.
Answer: C
Answer: (C) 66
Question: What is the speed required for a bike to cover a distance of 720 km in 12 hours?
(A) 50 kmh
(B) 40 kmh
(C) 100 kmh
(D) 60 kmh
(E) 80 kmh
Rationale: Speed= Distance / Time
Speed = 720 / 12 = 60
Answer: D
Answer: (D) 60 kmh
Question: If a positive integer n is divisible by both 2 and 5, then n must also be divisible by which of the following?
I. 10
II. 7
III. 40
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Rationale: A multiple of 2 and 5 is also a multiple of 10, but not necessarily a multiple of 7 or 40.
The answer is B.
Answer: (B) I only
Question: The list price of an article is Rs.70. A customer pays Rs.61.11 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 8%
(B) 7%
(C) 10%
(D) 3%
(E) 4%
Rationale: Explanation:
70*(90/100)*((100-x)/100) = 61.11
x = 3%
D
Answer: (D) 3%
Question: In a party attended by 9 persons, each clinch their glass with every other. How many glass clinches?
(A) 51
(B) 52
(C) 34
(D) 35
(E) 36
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=9*8/2
= 36
ANSWER:E
Answer: (E) 36
Question: Which of the following triples of numbers have the same standard deviation as the numbers p, q, and r?
I. p-2, q-2, r-2
II. 0, p-q, r-q
III. p-4, q+5, r-1
(A) I only
(B) II only
(C) I and III only
(D) II and I only
(E) I, II, and III
Rationale: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {p-2, q-2, r-2} is obtained by subtracting 2 from each term of {p, q, r}
Set {0, p-q, r-q} is obtained by subtracting s from each term of {p, q, r}
Set {p-4, q+5, r-1} is totally different from {p, q, r}.
Thus the answer is I and II only.
Answer:D.
Answer: (D) II and I only
Question: 5.40 can be expressed in terms of percentage as
(A) 5.04%
(B) 50.4%
(C) 209%
(D) 540%
(E) None of these
Rationale: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
5.40 * 100 = 540
Answer: Option D
Answer: (D) 540%
Question: If XY denotes X is raised to the power Y, Find the last two digits of 19413843+ 19614181
(A) 67
(B) 97
(C) 55
(D) 32
(E) 62
Rationale: 1721^3856
unit digit= 1^2=1
10th digit=5*6=30=0 means last two digit =1
and 1982^4181
unit digit=1
10th digit=8*2=16 mean last two digit= 61
hence,
61+1= 62
Answer: (E) 62
Question: What is the rate percent when the simple interest on Rs.780 amount to Rs.130 in 4 Years?
(A) 4.16
(B) 5.16
(C) 6.16
(D) 7.16
(E) 8.16
Rationale: 130 = (780*4*R)/100
R = 4.16%
Answer: A
Answer: (A) 4.16
Question: Find the fourth proportion to 2,3,6
(A) 18
(B) 12
(C) 9
(D) 3
(E) 4
Rationale: Explanation:
2:3 :: 6:x
=> 2/3 = 6/x
=> x = 18/2
=> x = 9
Option C
Answer: (C) 9
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,10,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) none
Rationale: Solution
Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share	=Rs.(210000×2/6)
= Rs.70000.
Answer C
Answer: (C) Rs.70,000