divelab/Sys2Bench huggingface dataset:
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 25% more than the price of the other, what is the price of each of these two oranges?
Options:
A)Rs 11.5, Rs 14.5
B)Rs 8, Rs 12
C)Rs 10, Rs 16
D)Rs 12, Rs 14
E)None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 25% of x) = Rs. x + 1/4x = Rs. 5x/4
So, x + 5x/4 = 26
9x = 104
x = 11.5
The prices of the two oranges are Rs. 11.5 and Rs. 14.5
Answer : A
Answer: A
Question: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 24, then which of the following could be a value of x?
Options:
A)-4
B)-3
C)2
D)3
E)1
Rationale: 5%x = (5+x)(5-x)
25-x^2 = 24
x^2 = 1
x=-1,1
Ans: E
Answer: E
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II. Regine
III. Brian
Options:
A)I only
B)II only
C)III
D)only I or II only
E)I, II, or III
Rationale: Let’s assume that Stephanie won the race in record time of 2.5 hrs. In that case
B = R + 0.5
Note that even if R took the minimum possible time of (2.6 hrs), then Brian would be 3.1 hrs and Stephanie would be 2.5 hrs. This case is very much possible. So S came first, then R and B came last.
The same is true with
B = S + 0.5
R came first, S and then B.
So we see that B is a loser in any case, however R or S have equal chances to win.
So (D) is the answer.
Answer: D
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 4 students left over. What is the sum of the two smallest possible values of n?
Options:
A)66
B)70
C)74
D)78
E)82
Rationale: n = 4k+1 = 7j+4
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+4.
1, 5, 9, 13, 17, 21, 25 = 7(3)+ 4
The next such number is 25 + 4*7 = 53.
25+53 = 78
The answer is D.
Answer: D
Question: The average of numbers 0.64204, 0.64203, 0.64202 and 0.64201 is ?
Options:
A)0.64202
B)0.64204
C)0.642022
D)0.642025
E)None
Rationale: Answer
Average = (0.64204 + 0.64203 + 0.64202 + 0.64201)/ 4
=2.5681/ 4
=0.642025
Correct Option: D
Answer: D
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 408 votes. Find the number of votes casted to the winning candidate?
Options:
A)288
B)1054
C)788
D)298
E)177
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 408
62% -------- ? => 1054
Answer: B
Answer: B
Question: The first republic day of the India was celebrated on 26th January,1950. It was
Options:
A)221
B)28
C)276
D)20
E)22
Rationale: 1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995.
Number of odd days till 1600 years = 0
1601 to 1700 = 5
1701 to 1800 = 5
1801 to 1900 = 5
49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days
25th January 1950 = 25/7 = 4 odd days
Total odd days =15 + 5 + 4 = 24/7 = 3 odd days
So 26th January,1950 is Thursday
Answer:B
Answer: B
Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?
Options:
A)3 hrs 15 min
B)3 hrs 45 min
C)4 hrs
D)4 hrs 15 min
E)4 hrs 45 min
Rationale: time taken by one tank to fill half the tank=4*(1/6)
Part filled by the four taps in 1 hour=4*(1/6)
remaining part=1/2
therefore 2/3:1/2::1:x
x=3/4hr=(3/4)*60=45min
total time =3 hr 45 min
ANSWER:B
Answer: B
Question: How much time does a train 100 metres long running at 72 km/hr take to pass a pole?
Options:
A)7.9s
B)2.5s
C)5s
D)7.6s
E)7.4s
Rationale: Explanation:
72 km/hr = 72 * 5/18 = 20 m/s
Speed = distance/time; v = d/t
20 = 100/t
t = 5s
ANSWER: C
Answer: C
Question: The sum of two numbers is 184. If one-third of the one exceeds one-seventh
of the other by 8, find the smaller number
Options:
A)53
B)18
C)68
D)112
E)72
Rationale: Let the numbers be x and (184 - x). Then,
(X/3) - ((184 – x)/7) = 8 => 7x – 3(184 – x) = 168 => 10x = 720 => x = 72.
So, the numbers are 72 and 112. Hence, smaller number = 72.
Answer is E.
Answer: E
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
Options:
A)2
B)5
C)6
D)7
E)None of these
Rationale: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
Answer:D
Answer: D
Question: There is a set consisting of 5 numbers--{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number?
Options:
A)1/5
B)1/4
C)1/3
D)1/2
E)4/5
Rationale: Total Number of possible subsets [ including Null Subset ] : 2525 -- (A number can occur or not occur in a subset -- 2 ways)
Possible subsets where 5 is not present [will include null subset] : 24∗124∗1.
P = 2424 / 2525 = 1 / 2.
ANSWER:D
Answer: D
Question: The number of positive integers valued pairs (x, y) ssatisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
Options:
A)fifty nine
B)57
C)55
D)58
E)60
Rationale: 4x-17y=1
y=(4x-1)/17
x has to be a positive integer such that 1<=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer
So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17
Lets try to observe the pattern
1. 3 mod 17 = 3
2. 7 mod 17 = 7
3. 11 mod 17 = 11
4. 15 mod 17 = 15
5. 19 mod 17 = 2
6. 23 mod 17 = 6
7. 27 mod 17 = 10
8. 31 mod 17 = 14
9. 35 mod 17 = 1
10. 39 mod 17 = 5
11. 43 mod 17 = 9
12. 47 mod 17 = 13
13.51 mod 17 = 0
14. 55 mod 17 = 4
15. 59 mod 17 = 8
16. 63 mod 17 = 12
17. 67 mod 17 = 16
... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)
So the right choices are x=13,13+17,13+17+17,.....
The number of such numbers is 59 (highest one being 999) A
Answer: A
Question: A man spends on an average Rs 269.47 for the first 7 months and Rs 281.05 for the next 5 months. Find his monthly salary if he saves Rs 308.46 during the whole year.
Options:
A)Rs 300
B)Rs 500
C)Rs 840
D)Rs 400
E)Rs 600
Rationale: Total spending in 12 months = Rs [269.47 x 7 - 281.05 × 5] = Rs 3,291.54
Total income = Spending + Saving
= Rs 3,291.54 + Rs 308.46
= Rs 3,600.00
Monthly salary = Rs 3600/12 = Rs 300
ANSWER:A
Answer: A
Question: At the library, 50 books were checked out that day from the display. 5 copies of Sandry's Book were checked out and 15 copies of Howl's Moving Castle. If only two other books were checked out (Harry Potter and the Lightning Thief) and they were both checked out in equal quantities, how many copies of the Lightning Thief were checked out?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: First, subtract the number of other books that were checked out from the total: 50-5-15=30. As the remaining two books were checked out in equal quantities, simply divide 30 by 2: 30/2=15. The answer is C, 15.
Answer: C
Question: During a clearance sale, a retailer discounted the original price of its TVs by 24% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
Options:
A)40%
B)45%
C)55%
D)60%
E)62%
Rationale: VERITAS PREPOFFICIAL SOLUTION:
D. With percent problems, the key is often to make sure that you take the percent of the correct value. In this case, the initial 25% off means that customers will pay 75% of the original price. Then for the second discount, keep in mind that the discount is taken off of the sale price, not of the original price. So that's 20% off of the 75% that they did pay, which can be made easier by looking at what the customer does pay: 80% of the 75% sale price. Using fractions, that means they pay: 4/5*(3/4) of the original price, which nets to 3/5 of the original price, or 62%.
E
Answer: E
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 7 skiers were CPR certified and 17 were not. How many skiers tried out for the ski patrol?
Options:
A)30
B)50
C)60
D)70
E)80
Rationale: Not Selected = 80%
If total is x.
Then 0.8x=7+17=24
x=30
Hence answer is A.
Answer: A
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.4 per sq m?
Options:
A)675, Rs.1350
B)575, Rs.1350
C)1350, Rs.675
D)675, Rs.2700
E)1550, Rs.875
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 4 = Rs.2700
ANSWER:D
Answer: D
Question: In 60 litres mixture milk and water are in the ratio 3:1. After adding how many liters of water its ratio will become 3:2
Options:
A)1
B)15
C)7
D)5
E)12
Rationale: Milk quantity = 3/4 * 60 = 45
water quantity = 60-45 = 15
new ratio of M:W = 45:15+x = 3:2
45+3x = 90
x = 15
Answer is B
Answer: B
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)33 1/6 %
B)33 8/3 %
C)33 1/3 %
D)73 1/3 %
E)33 16/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Answer: C
Question: From a group of 4 boys and 4 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?
Options:
A)1/2
B)2/3
C)3/5
D)4/7
E)5/9
Rationale: The total number of ways to choose 2 children from 8 is 8C2 = 28
The number of ways to choose 1 boy and 1 girl is 4*4 = 16
P(1 boy and 1 girl) = 16/28 = 4/7
The answer is D.
Answer: D
Question: 9 men can do a work in 12 days working 4 hours a day. In how many days can 6 men do the same work, working 8 hours a day?
Options:
A)18
B)9
C)10
D)8
E)11
Rationale: We have, M1D1H1 = M2D2H2
So, 9*12*4= 6*D2*8
D2 = 9*12*4/6*8 = 9
ANSWER:B
Answer: B
Question: Find the cost of fencing around a circular field of diameter 18 m at the rate of Rs.2.50 a meter?
Options:
A)138
B)132
C)150
D)140
E)222
Rationale: 2 * 22/7 * 9 = 56
56 * 2 1/2
= Rs.140
Answer: D
Answer: D
Question: With out any halt a train travels a certain distance with an average speed of 49 km ph , and with halts it covers the same distance at an average speed of 28 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
Options:
A)48 min.
B)45min.
C)15min.
D)18min.
E)19min.
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 49/28 = 7/4 = 105 minutes
:. 45 minutes is the halting time per hour
ANSWER:B
Answer: B
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Options:
A)3/4
B)3/8
C)3/1
D)3/2
E)3/9
Rationale: Explanation:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3,4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) = n(E)/n(S) = 27/36 = 3/4.
Answer: A) 3/4
Answer: A
Question: In traveling from a dormitory to a certain city, a student went 1/2 of the way by foot, 3/5 of the way by bus, and the remaining 4 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
Options:
A)20
B)15
C)40
D)10
E)12
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/2x + 3/5x + 4
x - 1/2x - 3/5x = 4
x=20km
Option: A
Answer: A
Question: When positive integer A is divided by positive integer B, the result is 5.15. Which of the following could be the integer A is ?
Options:
A)107
B)117
C)103
D)123
E)171
Rationale: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.15
0.15 = 15/100 = 3/20 so possible remainders are 3,6,12,9,15.
let remainder is 3
Now when we divide option C i.e 103/20 = 5 is quotient and remainder is 3
therefore ans - C
Answer: C
Question: Three positive integers a, b, and c are such that their average is 80 and a ≤ b ≤ c. If the median is (a + 20), what is the least possible value of c?
Options:
A)88
B)89
C)90
D)92
E)94
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 80
So, a+b+c3a+b+c3 = 240 or a + b + c = 240
a ≤ b ≤ c
Median = (a + 20)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 20
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 20) + (a + 20) = 240 (b and c are equal and b, the median, is a + 20)
Or 3a = 200 or a = 66.66
So, b = c = 66.66+ 20 = 86.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 20) + (a + 21) = 240
Or 3a = 199. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 20) + (a + 22) = 240
Or 3a = 198 or a = 66
If a = 66, b = 86 and c = 88.
The least value for c that satisfies all these conditions is 88.
Correct answer is choice A.
Answer: A
Question: A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 8 books for a total of $38.00, and on Tuesday the store sold 20 maps and 12 books for a total of $60.00. At this store, how much less does a map sell for than a book?
Options:
A) $0.25
B) $0.50
C) $0.75
D) $1.00
E) $l.25
Rationale: 12x+8y=38
20x+12y=60
multiply eq 1 by 5 and eq 2 by 3
60x+40y=38*5
60x+36y=60*3
subtracting 1 from 2
4y=190-180
y=2.5
therefore
x=1.5
difference in price =1
D
Answer: D
Question: David buys an old scooter for Rs. 2400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 3600, his gain percent is :
Options:
A)20%
B)12%
C)10%
D)5%
E)None of these
Rationale: Explanation :
Solution: C.P. =Rs. (2400+600) =Rs. 3000; S.P. = Rs. 3600.
Gain% = (600*100/3000) = 20%.
Answer : A
Answer: A
Question: Mr. George paid $8,000 for 100 shares of stock A and $6,000 for 100 shares of stock B. He later sold the same shares of both stocks, gaining 3/8 the amount he paid for stock B. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
Options:
A)A loss 1 1/2 times as much.
B)A loss 2 times as much
C)The same.
D)A gain 1 1/2 times as much.
E)A gain 1.33 times as much.
Rationale: A = 8000; B = 6000; Profit = (3/8)*6000 = 2250
After prices are reversed:
A = 6000; B =8000; Profit = (3/8)*8000 = 3000
3000 --> Gain of 1.33 times 2250
Answer: E
Answer: E
Question: A gold purification process cycle, is able to remove 1/16 of impurities in gold. If we have a 10 grams of gold ore dust containing 16/24 pure gold. How much impurities would have been removed from that old after 4 cycles of purification using that method?
Options:
A)0.72
B)0.74
C)0.76
D)0.78
E)0.82
Rationale: X is the initial quantity of impurities in that gold.
After a cycle of purification the quantity of impurities left would be X1=X-1/16X i.e. X1=15/16X
Same thing for X2, X3, X4, respectively representing the quantity of impurities left after 2, 3, 4 cycles of purification.
So we have:
X1=15/16 X
X2=15/16 X1
X3=15/16 X2
X4=15/16 X3
By multiplying both ends of the equations we get:
X1*X2*X3*X4 = (15/16)^4 X*X1*X2*X3
Simplification leaves us with:
X4 = (15/16)^4 X
X4 is the quantity of impurities left after four cycles. So the cumulative quantity of impurities (Q4) which has been removed after 4 cycles is: Q4= X-X4=X-(15/16)^4X i.e. Q4 = X (1-(15/16)^4)
In this case, given X was: X=(1-16/24) * 10 g = 3.33 g (Remember we had 16/24 pure gold)
So we have Q4 = 3.33 * (1-(15/16)^4) = 3.33 * (1-(50625/65536)) = 3.33 * (14911/65536) = 0.757 rounded gives Q4=0.76
Answer: C
Answer: C
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $200, by what percent is the price to be reduced?
Options:
A)10%
B)15%
C)20%
D)25%
E)40%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $200
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (200)*100 / 500 = 40%
Answer: Option E
Answer: E
Question: One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 150cm when it touches the floor on third time. What is the value of the original height?
Options:
A)60cm
B)90cm
C)100cm
D)120cm
E)130cm
Rationale: when Ball comes down, Then i have indicated the distance covered in green
when Ball goes up, Then i have indicated the distance covered in red
Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h
h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 150
2.5 h = 150
h = 60.
A is the answer.
Answer: A
Question: If the price of gold increases by 25%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)331/8%
B)331/3%
C)631/3%
D)332/3%
E)20%
Rationale: 100
125
------
125-------25
100-------? => 20%
Answer:E
Answer: E
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-9) = 0, then f(x) crosses the y-axis at what y-coordinate?
Options:
A)-9
B)-1
C)0
D)1
E)9
Rationale: When x = 1 and when x = -9, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+9)
f(0) = -9
The answer is A.
Answer: A
Question: In triangle PQR, the angle Q = 90 degree, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
Options:
A)1.6 cm
B)2.4 cm
C)4.8 cm
D)2.16 cm
E)3.2 cm
Rationale: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:2=8:10 --> QY=1.6.
Answer: A.
Answer: A
Question: A boat having a length 5 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Options:
A)100 kg
B)60 kg
C)72 kg
D)96 kg
E)None of these
Rationale: Explanation:
Volume of water displaced = (5 x 2 x 0.01) m3
= 0.10 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.10 x 1000)kg
= 100 kg.
Answer: A
Answer: A
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $250, by what percent is the price to be reduced?
Options:
A)10%
B)15%
C)50%
D)25%
E)30%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $250
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (250)*100 / 500 = 50%
Answer: Option C
Answer: C
Question: The triplicate ratio of 1:4 is?
Options:
A)1:64
B)1:8
C)1:7
D)1:2
E)1:1
Rationale: 13: 43 = 1:64
Answer: A
Answer: A
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations X are possible?
Options:
A)3
B)4
C)5
D)6
E)X=8
Rationale: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6), (48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.E
Answer: E
Question: The respective ages of father and his son are 51 and 16 years. In how many years will the father be twice as old as his son ?
Options:
A)19 years
B)9 years
C)10 years
D)15 years
E)12 years
Rationale: Suppose x years later the father will be twice as old as his son.
x + 51 = 2 (x + 16)
x = 51 - 32 = 19 years
answer : A
Answer: A
Question: What inequality represents the condition 1<x<13?
Options:
A)|x|<3
B)|x+5|<4
C)|x-7|<6
D)|-5+x|<4
E)|3+x|<5
Rationale: 1<x<13 represents segment with
length: 13-1 = 12
center: (13+1)/2 = 7
For any |x-a|<b a is a center and b is a half of length. So, |x-7|<12/2 represents our inequality (answer C)
Answer: C
Question: It takes one machine 4 hours to complete a production order and another machine 9 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
Options:
A)a) 7/12
B)b) 2 10/13
C)c) 1 5/7
D)d) 3 1/2
E)e) 7
Rationale: RT = W
Given:
R = 1/9 + 1/4 = 13/36
T = ?
W = 1
T = 1 / (13/36) = 36/13 = 2 10/13
Answer: B
Answer: B
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $231 for it, the cost price of the Cricket Bat for A is:
Options:
A)150
B)120
C)154
D)160
E)210
Rationale: 125% of 120% of A = 231
125/100 * 120/100 * A = 231
A = 231 * 2/3 = 154.
ANSWER C
Answer: C
Question: 1/[(1/0.03) + (1/0.37)] = ?
Options:
A)0.004
B)0.02775
C)2.775
D)3.6036
E)36.036
Rationale: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
1/36 = .02 something
Answer (B)
Answer: B
Question: A basket has 5 apples and 7 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
Options:
A)2/7
B)4/11
C)5/11
D)7/22
E)15/44
Rationale: The total possible choices are 12C3 = 220
The ways to choose 3 apples: 5C3 = 10
The ways to choose 2 apples: 5C2 * 6C1 = 60
P(at least 2 apples) = 70/220 = 7/22
The answer is D.
Answer: D
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open,in how many hours will the tank be filled ?
Options:
A)2
B)2.5
C)3
D)3.5
E)4
Rationale: 1/5+1/10+1/30=10/30=1/3. soo 3 hrs
ANSWER:C
Answer: C
Question: A seven-digit phone number is divisible by 5. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code?
Options:
A)05.
B)06.
C)03.
D)04.
E)02.
Rationale: Given that 7 digit number is divisible by 5
we know any number will not be divisible by 5 if the sum of all digits of the number is not the multiple of5.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 5... hence answer is A
Answer: A
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
Options:
A)450
B)750
C)130
D)250
E)200
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1]
= 200.
Ans: E
Answer: E
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 2 inches tall. How tall are the sculpture andbase together?
Options:
A)3.1 feet
B)3.2 feet
C)3.3 feet
D)3.0 feet
E)3.5 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+2=36
36/12=3.0 feet
ANSWER:D
Answer: D
Question: When Q is divided by W, the quotient is R and the remainder is r. Which of the following expressions is equal to r?
Options:
A)RW + Q
B)Q - RW
C)RW - Q
D)QW - R
E)Q/R
Rationale: Q/W = R + r/W
Q -RW = r
Amswer: B
Answer: B
Question: If a coin is tossed twice what is the probability that it will land either heads both times or tails both times?
Options:
A)1/8
B)1/6
C)1/4
D)1/2
E)1
Rationale: Prob to get 2 heads = 1/2*1/2 = 1/4
Prob to get 2 tails = 1/2*1/2 = 1/4
So, Prob to get either 2 heads or 2 tails = 1/4+1/4 = 1/2
Answer will be D.
Answer: D