Datasets:
thewordsmiths
/
stem_mcqa

Dataset card Data Studio Files Community
2
subject
stringclasses
1 value
question
stringlengths
3
1.14k
options
listlengths
5
5
solution
stringlengths
18
3.7k
answer
stringclasses
5 values
mathematics
A bank pays interest to its customers on the last day of the year. The interest paid to a customer is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $6840. What is the average monthly balance maintained by John in his account during the year?
[ "2840", "5680", "6840", "7540", "34200" ]
Soln:- Bank balance is doubled with accumulation of interest to 6840.. this means INTEREST is 6840/2=3420 for entire year.. although since interest is 10% of avg MONthly balance, it becomes 34200.. ANSWER:E The answer is: E
E
mathematics
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
[ "2.99", "2.88", "2.91", "2.77", "2.11" ]
M = 6 S = 1.2 DS = 6 + 1.2 = 7.2 US = 6 - 1.2 = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 Answer:B The answer is: B
B
mathematics
Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 9 minutes 42 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
[ "3%", "5%", "8%", "9%", "12%" ]
Bob's time = 640 secs. His sis' time = 582 secs. Percent increase needed = (640-582/640) * 100 = 58/640 * 100 = 9%. Ans (D). The answer is: D
D
mathematics
If 6 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
[ "-7", "-4", "-3", "-9", "6" ]
The phrase “6 is one solution of the equation” means that one value of x is 6. Thus, we first must plug 6 for x into the given equation to determine the value of k. So we have 6^2 + (3)(6) + k = 10 36 + 18 + k = 10 54 + k = 10 k = -44 Next we plug -44 into the given equation for k and then solve for x. x^2 + 3x – 44 = 10 x^2 + 3x – 54 = 0 (x+9)(x-6) = 0 x = -9 or x = 6 Thus, -9 is the other solution. Answer D. The answer is: D
D
mathematics
-20 , -16 , -12 , -8 .... In the sequence above, each term after the first is 6 greater than the preceding term. Which of the following could not be a term in the sequence?
[ "0", "200", "444", "660", "780" ]
Ans :B Since 200 is not divisible by 6 , all the other options are divisible by 6 The answer is: B
B
mathematics
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
[ "65 km/hr", "50 km/hr", "21 km/hr", "25 km/hr", "76 km/hr" ]
Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B The answer is: B
B
mathematics
A building of 6 floors is being painted by 2 painters, and they take 3 days to paint the first floor. If 3 men are then added to the work and all of them continue painting at the same rate, how many days take to them paint all the building, since the first day?
[ "5 days", "8 days", "9 days", "10 days", "12 days" ]
We have that: 2 painters ----- 3 days, (2+3) P ----- X d, that is: (X d/ 2P) = (3 d/5P), then: X d = (3 d/5P)2P = (6/5)d. Is to say, the 5 painters paint the same quantity in 6/5 days; as it is only 1/6 of the building, all the building would be: B = 3 d + 5(6/5) d = (3 + 6) d = 9 days. Answer C. The answer is: C
C
mathematics
A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
[ "3/105", "3/103", "1/108", "2/113", "2/115" ]
Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108 C The answer is: C
C
mathematics
Number of prime numbers between 20 and 60 is
[ "4", "5", "6", "7", "9" ]
total 9=23, 29, 31, 37, 41, 43, 47, 53, 59 ANSWER:E The answer is: E
E
mathematics
Simplify:(4x2 - 2x) - (-5x2 - 8x)
[ "2x(3x + 2)", "4x(3x + 2)", "2-(3x + 2)", "3x(3x - 2)", "3x(3x + 2)" ]
(4x2 - 2x) - (-5x2 - 8x) = 4x2 - 2x + 5x2 + 8x. = 4x2 + 5x2 - 2x + 8x. = 9x2 + 6x. = 3x(3x + 2). Answer: (E) 3x(3x + 2) The answer is: E
E
mathematics
In a class of students, the ratio of girls to boys is 1:2. If 2 more girls joined the class, the ratio would be 2:3. How many students are in the class?
[ "18", "20", "22", "24", "26" ]
Let x be the number of students in the class. (1/3)*x=(2/5)(x+2)-2 5x=6x+12-30 x=18 The answer is A. The answer is: A
A
mathematics
How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
[ "65", "77", "32", "32", "60" ]
The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit. Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = 5P3 = 60. Answer:E The answer is: E
E
mathematics
In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
[ "54.3 kg", "55.5 kg", "66.5 kg", "67.8 kg", "69 kg" ]
Let Mike's weight be X kg. According to Mike, 65 < X < 72. According to Mike's brother, 60 < X < 70. According to Mike's mother, X < 68. The values satisfying all the above conditions are 66 and 67. Required average = (66 + 67) / 2 = 66.5 kg D The answer is: D
D
mathematics
Using all the letters of the word "NOKIASED", how many words can be formed, which begin with N and end with A?
[ "800", "720", "900", "300", "100" ]
There are five letters in the given word. Consider 8 blanks .... The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 6! ways. The number of words = 6! = 720. Answer:B The answer is: B
B
mathematics
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
[ "3100", "210", "21300", "25200", "24400" ]
Number of ways of selecting 3 consonants from 7 =7C3 Number of ways of selecting 2 vowels from 4 = 4C2 Number of ways of selecting 3 consonants from 7 and 2 vowels from 4 = 7C3 × 4C2 = 210 It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels). Number of ways of arranging 5 letters among themselves =5! = 5*4*3*2*1 = 120 Hence, required number of ways=210×120=25200 option - D The answer is: D
D
mathematics
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?
[ "4", "8", "12", "16", "20" ]
4 pairs = 4*2 = 8 people total 8C4 = 8!/4!4! = 70 total outcomes Total – unfavorable = favorable Unfavorable outcomes Assuming one pair of twins in the committee, we have two spaces left. Since we plugged a pair of twins in the committee, we have 8-2= 6 people to fill 2 spaces. 6C2 = 6!/2!4! = 15 ways to fill the two remaining slots We only filled the slots with one pair, and we have to account for arrangements of the pairs. Now, we have 4 pairs. 4*15= 60 total arrangements When we place members into the remaining slots, there may be an additional set of twins. There are 2 remaining slots to which we can fit a pair of twins. If it were one remaining slot, we cannot fit a pair of twins, so we wouldn’t have to account for duplicates. Now we account for the number of duplicates. # of duplicates = Total arrangements - # of unique combinations To find the # of duplicates of twins, we need treat a pair of twins as one unit. This means the 4 slots are really 2 slots. Total ways of arranging four pairs of twins in two slots 4P2 = 4*3 = 12 total ways Total # of unique combinations Choosing two pairs out of 4 pairs = 4C2 = 6 Therefore, # of duplicates = 12 - 6 = 6 duplicates 70 – 60 + 6 = 16 ANS:D The answer is: D
D
mathematics
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
[ "3.34", "45", "44", "33", "77" ]
Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2 = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) } = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m Answer: Option A The answer is: A
A
mathematics
The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is :
[ "240", "270", "295", "360", "None" ]
Solution Let the numbers be x and (x + 1365). Then, x + 1365 = 6x + 15 ⇔ 5x = 1350 ⇔ x = 270. Answer B The answer is: B
B
mathematics
Which one of the following is not a prime number?
[ "31", "61", "71", "91", "98" ]
91 is divisible by 7. So, it is not a prime number. Answer: Option D The answer is: D
D
mathematics
If points A and B are (10-5) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB
[ "I only", "II only", "III only", "I and II only", "I and III only" ]
I. The area of a square region with side AB --> side=AB=(10-5) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. The answer is: A
A
mathematics
40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple?
[ "47", "46", "54", "58", "62" ]
orange+mango-apple=7 mango+apple-orange=10 apple=40 orange+mango+apple=4 40+10+4-7=47 like apple ANSWER:A The answer is: A
A
mathematics
AMS employs 7 professors on their staff. Their respective probability of remaining in employment for 10 years are, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years all 7 of them still work in AMS is ?
[ "0.19", "0.018144", "0.1", "0.16", "none of these" ]
Asking atleast 6 of them continue , it has 3 cases. 1 all 7 professors continue. all 7 continues - 0.3*0.4*.0.5*0.6*0.7*0.8*0.9 =0.018144 B The answer is: B
B
mathematics
12,31,68,129,?,347,516
[ "129", "240", "347", "220", "520" ]
2*2*2 + 4 = 12 3*3*3 +4 = 31 4*4*4 + 4 = 68 5*5*5 + 4 = 129 7 *7 *7 + 4 = 347 8 *8 *8 + 4 = 516. 6*6*6 + 4 = 220 ANSWER : D The answer is: D
D
mathematics
The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is
[ "11 : 9", "11 : 18", "21 : 19", "21 : 19", "None" ]
Sol. Let the numbers be x and y. Then, x+y / x -y = 40/4 = 10 ⇔ (x+y) = 10(x-y) ⇔ 9x = 11y ⇔ x/y = 11 / 9. Answer A The answer is: A
A
mathematics
Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
[ "100", "110", "120", "125", "130" ]
4x 5x 6x 100 50 25 400x + 350x + 150x = 16000 x = 20 6x = 120 ANSWER C The answer is: C
C
mathematics
In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 3/4 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and curved
[ "1/8", "1/6", "1/4", "3/4", "7/8" ]
Good question. So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved). We're told that 3/4 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/4 are yellow. We're also told there is an equal probability of straight or curved, 1/2. We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ). So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(curved) = 1/4 * 1/2 = 1/8, or A. The answer is: A
A
mathematics
When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale?
[ "44% increase", "44% decrease", "66% increase", "75% increase", "None of these" ]
Let the original price be x and sale be of y units. Then, the revenue collected initially = x × y Now, new price = 0.8x, new sale = 1.8y Then, new revenue collected = 1.44xy % increase in revenue = 0.44xy/xy×100 = 44% increase Answer A The answer is: A
A
mathematics
What will be the cost of building a fence around a square plot with area equal to 289 square feet, if the price per foot of building the fence is Rs. 58?
[ "3944", "3932", "3929", "3926", "3902" ]
Let the side of the square plot be a foot a2 = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 foot Cost of building the fence = 68 * 58 = Rs.3944. Answer:A The answer is: A
A
mathematics
A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1251. Find the number to be multiplied.
[ "130", "132", "134", "136", "139" ]
Let the required number be x. Then, 43x – 34x = 1251 or 9x = 1251 or x = 139. Required number = 139. ANSWER:E The answer is: E
E
mathematics
Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 600meters, after what time will they meet at the starting point?
[ "20sec", "15sec", "30sec", "50sec", "40min" ]
They meet every 600/7+8 = 40sec Answer is E The answer is: E
E
mathematics
If n ≠ 0, which of the following must be greater than n? I. n^4 II. 2n III. 2 - n
[ "I only", "II only", "I and II only", "II and III only", "None" ]
n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only I =>answer is A The answer is: A
A
mathematics
Evaluate 24.39 + 562.093 + 35.96
[ "631.344", "622.443", "623.434", "632.423", "632.443" ]
24.39 + 562.093 + 35.96 = 622.443 Option B The answer is: B
B
mathematics
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is?
[ "4452", "4445", "4330", "4334", "4336" ]
Divisor = (5 * 42) = 210 = 10 * Quotient = Divisor => Quotient = 210/10 = 21 Dividend = (Divisor * Quotient) + Remainder Dividend = (210 * 21) + 42 = 4452 A The answer is: A
A
mathematics
electric running buzzer rang after every 60 sec.and second buzzer rang after every 62 sec.both rung together at 10'o clock.after that at what time both rang together?
[ "morning 10:30", "morning 10:31", "morning 10:59", "morning 11:00", "none of these" ]
difference of time between together ringing of buzzer=l.c.m of 60 sec. and 62 sec. (2*30*31) sec.={2*30*31}/60=31 minute hence,next time they rang together at morning 10:31 answer B The answer is: B
B
mathematics
In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 80% people got computers and 80% got Air-conditionor. how many people(minimum) got all these luxury.
[ "23%", "17%", "11%", "10%", "15%" ]
D 10% 100 - [ (100-85)+(100-80)+(100-75) +(100-70)] =100-(15+20+25+30) =100-90 The answer is: D
D
mathematics
If equation |x/5| + |y/5| = 2 encloses a certain region on the coordinate plane, what is the area of this region?
[ "20", "50", "200", "100", "400" ]
The equation can be reduced to intercept form as |x/10| + |y/10| = 1, so these are lines in four quadrants with x and y intercept as 10, so it is a rhombus with diagonals of 20 each and hence area = 1/2*d1*d2 = 1/2*20*20 = 200. Answer C. The answer is: C
C
mathematics
If logn48 = a and logn108 = b. What is the value of logn1296 in terms of a and b?
[ "2(2a + b)/5", "(a + 3b)/5", "4(2a + b)/5", "2(a + 3b)/5", "None of these" ]
Given logn48 = 4logn2 + logn3 = a and logn108 = 2.logn2 + 3logn3 = b Let logn 2 = X and logn3 = Y. => 4X + Y = a 2X +3Y = b. 2 x (ii) - (i) gives 6Y - Y = 2b - a Y = (2b - a)/5 Similarly, X = (3a - b)/10. logn1296 = 4(logn2 + logn3). = 4[(2b - a)/5 + (3a - b)/10]. = 4[(a + 3b)/10] = 2(a + 3b)/5. ANSWER:D The answer is: D
D
mathematics
A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 0, what is the value of x?
[ "-4 and 0", "-2", "2", "4", "Cannot be determined." ]
A number x is multiplied with itself --> X^2 added to the product of 4 and x --> X^2+4X If the result of these two operations is 0 --> X^2+4X=0 i.e X^2+4X=0 is the Quadratic equation which needs to be solved. X(X+4) = 0 Hence X=0. X=-4 IMO A The answer is: A
A
mathematics
What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
[ "148", "150", "152", "158", "160" ]
D = d * Q + R D = 17 * 9 + 5 D = 153 + 5 D = 158 The answer is: D
D
mathematics
46080, 3840, 384, 48, 8, 2, ?
[ "0.5", "1", "1.5", "2", "2.5" ]
46080 ÷ 12 = 3840 3840 ÷ 10 = 384 384 ÷ 8 = 48 48 ÷ 6 = 8 8 ÷ 4 = 2 2 ÷ 2 = 1 Answer is B. The answer is: B
B
mathematics
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
[ "60", "34", "75", "87", "94" ]
A + B + C = 3 *84 = 252 A + B + C + D = 4 * 80 = 320 ---- (i) So, D = 68& E = 68 + 3 = 71 B + C + D +E = 79 * 4 = 316 --- (ii) From Eq. (i) & (ii) A-E = 320 – 316 = 4 A = E +4 = 71 + 4 = 75 C The answer is: C
C
mathematics
A train 100 m long pass a telegraph pole in 5 seconds. Find the speed of the train
[ "66 km/hr", "68.4 km/hr", "72 km/hr", "79.2 km/hr", "None" ]
Sol. Speed = [100/5] m/sec = [20 * 18/5] km/hr = 72 km/hr. Answer C The answer is: C
C
mathematics
If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 5x+ 5y >5z III. yz > xz IV. xy > y + z
[ "I only", "II only", "II and III only", "II and IV only", "III and IV only" ]
we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 5x+ 5y >5z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B The answer is: B
B
mathematics
When sold at a 50% discount, a sweater nets the merchant a 40% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?
[ "20%", "64.29%", "70%", "80%", "100%" ]
we should be careful about what are we measuring % on/what is the base.. let the Marked up price =100.. Selling price= 100-50%of 100=50.. profit= 40%.. therefore the wholesale purchase cost= x.... 1.4x=50 or x=35.71... marked price was 100 so ... so answer is 64.29%.. B The answer is: B
B
mathematics
When average age of 21 members are 0, how many members greater than 0?
[ "17", "20", "21", "24", "25" ]
Average of 21 numbers = 0. Sum of 21 numbers (0 x 21) = 0. It is quite possible that 20 of these numbers may be positive and if their sum is a then 21st number is (-a) Answer is 20 (B) The answer is: B
B
mathematics
Look at this series: 7, 10, 8, 11, 9, 12, 10, 13, ... What number should come next?
[ "10", "11", "12", "13", "14" ]
This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted. The answer is B. The answer is: B
B
mathematics
If ty > 0 and yz < 0, which of the following must be negative:
[ "tyz", "ty(z^2)", "t(y^2)z", "t(y^2)(z^2)", "(x^2)(y^2)(z^2)" ]
ty > 0 means that ty is positive. yz < 0 means that yz is negative. t(y^2)z = (ty)(yz) = positive*negative = negative. Thus option C is always negative. The answer is: C
C
mathematics
Rahul's housing colony have One tap, working alone at its maximum constant rate, can fill a certain tank in 230 seconds. A second tap, working alone at its maximum constant rate, can fill the same tank in 234 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the tank is closest to
[ "116 seconds", "150 seconds", "177 seconds", "200 seconds", "270 seconds" ]
Tap 1 : 230 secs Tap 2 : 234 secs Considering the average of these 2 taps : 232 secs. So 1 tap can fill the tank in 232 secs, so 2 taps can fill the tank in 232/2 = 116 secs. Closest answer is A. The answer is: A
A
mathematics
In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
[ "209", "210", "230", "235", "240" ]
Option 'B' 7p3 = 7 × 6 × 5 = 210 The answer is: B
B
mathematics
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *9 + 3 and *9 + 9, inclusive?
[ "None", "One", "Two", "Three", "Four" ]
Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *9 would be divisible by all numbers from 1 to 9. => *9+3 would give me a number which is a multiple of 3 and therefore divisible (since *9 is divisible by 3) In fact adding anyprimenumber between 1 to 9 to *9 will definitely be divisible. So the answer is none (A)! Supposing if the question had asked for prime numbers between *9 + 3 and *9 + 11 then the answer would be 1. For *9 +3 and *9 + 13, it is 2 and so on... A The answer is: A
A
mathematics
How much interest will $10,000 earn in 3 months at an annual rate of 6%?
[ "$250", "$150", "$450", "$550", "$650" ]
Soln:- 6 months = 1/4 of year; 6% = 6/100=3/50; $10,000(principal)*3/50(interest rate)*1/4(time)=$150. ANSWER:B The answer is: B
B
mathematics
For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 25 true?
[ "1", "3", "5", "2", "9" ]
Answer D (a+b)(a-b)=25 5cases For (a+b), (a-b) 25, 1 5, 5 Answer D The answer is: D
D
mathematics
Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 15 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
[ "11.", "12.", "13.", "18.", "14.5" ]
Price of candy before price increase= 10/1.25= 8 Price of soda before price increase= 15/1.5= 10 Total price = 8+10= 18 D is the answer The answer is: D
D
mathematics
In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam?
[ "100", "120", "110", "130", "160" ]
Explanation : Number of student = (84-64) * 94/18.8 = 100 Answer : A The answer is: A
A
mathematics
The diagonals of a rhombus are 22 cm and 30 cm. Find its area?
[ "358", "329", "350", "330", "317" ]
1/2 * 22 * 30 = 330 Answer:D The answer is: D
D
mathematics
A bag contains 5 white marbles and 5 red marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
[ "1/6", "1/35", "1/3", "1/462", "1/126" ]
first, total ways to select for all boys and girls, i.e 10!/(5!*5!) = 252 then there are one two way girls can have all same colors, either white or red. The number of ways in which 5 girls can select 5 white balls = 5C5 = 1 The number of ways in which 5 girls can select 5 red balls = 5C5 = 1 Therefore, total favorable outcomes/total outcomes = 2/252= 1/126 E The answer is: E
E
mathematics
John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
[ "30 ml", "40 ml", "70 ml", "90 ml", "100 ml" ]
concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =310 By rule of alligation, concentration of water in mixture1 (29) concentration of water in pure water (1) Mean concentration (310) 1−310=710 310−29=790 => Quantity of mixture1 : Quantity of water =710:790=110:190=1:19 Given that Quantity of mixture1 = 630 ml => 630 : Quantity of water =1:19 => Quantity of water =630×19=70 ml C The answer is: C
C
mathematics
If (x^2 + 1)y=5, which of the following is not a possible value for y?
[ "1/2", "2", "4/3", "3", "13/2" ]
Its simple equation is (x^2 +1)y = 5 ===> x^2 = (5/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS. Hence, (5/y) - 1>= 0 ===> y =< 5. Now only option E has greater value of 'y' than 5. Thus, correct ans is E The answer is: E
E
mathematics
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
[ "30 birds", "60 birds", "72 birds", "90 birds", "84 birds" ]
Explanation: Let the no of shots be x. Then, Shots fired by A = 5/8x Shots fired by B = 3/8x Killing shots by A = 1/3 of 5/8x= 5/24x shots missed by B =1/2 of 3/8x =3/16x therefore, 3/16x=27=> x=144 Birds killed by A = 5/24x=(5/24)x144=30 ANSWER IS A The answer is: A
A
mathematics
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
[ "5.79", "5.71", "5.76", "5.79", "5.73" ]
M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76 Answer: C The answer is: C
C
mathematics
A train leaves New York City at 7.15 Am and arrives in Buffalo at 2.47 that afternoon. What total length of time does the trip take?
[ "7 h 92 min.", "7 h 32 min.", "7 h 12 min.", "8 h 32 min.", "5 h 32 min." ]
Explanation: 2.47 PM = 14.47 Total time = 14.47 – 7.15 = 7 hrs 32 min Answer:B The answer is: B
B
mathematics
Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
[ "350", "370", "390", "430", "None" ]
Explanation: Assumed mean = Rs. 350 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. 350 + Rs. 40 = Rs. 390 Correct Option: C The answer is: C
C
mathematics
A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
[ "1/20", "1/12", "1/5", "4/21", "5/21" ]
series : a1, a2....a20,n sum of a1+a2+...+a20 = 20*x (x = average) so, n = 2*x Hence, a1+a2+..+a20+n = 22x So, the fraction asked = 2x/22x = 1/12 B The answer is: B
B
mathematics
When a train travels at a speed of 70kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
[ "37.5km", "50.5km", "60km", "85.5km", "95km" ]
Let x be the time reached with the speed 70km/h 50km/h ----> x+15 Distance is equal so 70(km/h)× xhr = 50(km/h) × (x+15) hr So 70 x = 50x + 750 So the would be in km And x = 37.5 ANSWER:A The answer is: A
A
mathematics
In how many ways can the letters of the word "COMPUTER" be arranged?
[ "36480", "40320", "44290", "48360", "52810" ]
The total ways of arranging the letters = 8! = 40320 The answer is B. The answer is: B
B
mathematics
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
[ "33 1/6", "33 1/9", "33 1/3", "33 1/2", "33 1/23" ]
675 ---- 225 100 ---- ? => 33 1/3% Answer: C The answer is: C
C
mathematics
If (2x + 1) times (x + 2) is an odd integer, then x must be:
[ "an odd integer", "an even integer", "a prime number", "a composite number", "a negative integer" ]
Solution: (2x + 1) times (x + 2) means (2x + 1)(x + 2) (2x + 1)(x + 2) = 2x^2+5x+2 For 2x^2+5x+2 to be odd, 5x+2 must be odd since 2x^2 is always even. So 5x must be odd, hence x must be odd. Therefore x is an odd integer. Answer: A The answer is: A
A
mathematics
Vijay bought 160 shirts at the rate of Rs. 215 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
[ "s.225", "s.288", "s.485", "s.273", "s.282" ]
Total CP per shirt = 215 + 1400/160 + 1.75 + 320/160 = Rs. 227.5 SP = CP[(100 + profit%)/100] = 227.5 * [(100 + 20)/100] = Rs.273. Answer:D The answer is: D
D
mathematics
Tough and Tricky questions: Number Properties. What is the smallest positive integer x such that 500x is the cube of a positive integer?
[ "2", "3", "5", "10", "15" ]
We want to know the smallest x that will make 500x a CUBE of some number. Let's call that number y. Let's first figure out what we're working with. The prime factorization of 500 can be visualized: ...........500 ......../.......\ ......50.......10 ...../..\....../...\ ...25...2...2.....5 .../..\ ..5....5 So, we have 5 * 5 * 5 * 2 * 2 that can be multiplied together to get 500. Now we need to figure out what we need to make 450 * x into a cube of y (y^3=500*x). We have two 5s, two 3s, and one 2. To arrange these numbers in identical sets (2,5), we need at least one more 2. Each of these numbers will give us the value of y (2*5=10), which, multiplied by itself three times, gives us 500 * x. Looking at the factors we need to complete the sets, we get x= 2. We know this is the smallest number possible because prime factors by definition cannot be broken down any further. Therefore, we can go with answer choice A. If time permits, we can do a sanity check. We calculated that y should be 2 * 5, or 10. 10 * 10 * 10 = 1000. Also, 500 * 2 = 1000. The answer is: A
A
mathematics
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 10 cm.
[ "190 cm2", "885 cm2", "285 cm2", "825 cm2", "725 cm2" ]
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (10) = 190 cm2 Answer: A The answer is: A
A
mathematics
A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
[ "1909", "1900", "1908", "1901", "1902" ]
65 * 6 : 84 * 5 : 100 * 3 26:28:20 C share = 74000 * 95/100 = 7030 * 20/74 => 1900 Answer: B The answer is: B
B
mathematics
In how many ways a committee, Consisting of 4 men and 5 women can be formed from 8 men and 10 women?
[ "2660", "3360", "11760", "17640", "17200" ]
To choose Required number of ways to form a committee: Select 4 men out of 8 men and 5 women out of 10 women. That is 8C4 * 10C5. 8C4=8!/4!*4!=70 10C5=10!/5!*5!=252 The Required number of ways=70*252=17640 D The answer is: D
D
mathematics
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 35 cm?
[ "276 sq.cm", "268 sq.cm", "618 sq.cm", "297 sq.cm", "700 sq.cm" ]
Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus. BE2 + AE2 = AB2 252 = 152 + AE2 AE = √(625 - 225) = √400 = 20, AC = 20 + 20 = 40 cm. Area of a rhombus = 1/2 * d1d2 = 1/2 * 40 * 35 = 700 sq.cm. Answer:E The answer is: E
E
mathematics
Two boys starts from the same place walking at the rate of 4 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 10.5 km apart?
[ "8", "5", "7", "9", "6" ]
Explanation: Relative speed = 5.5 - 4 = 1.5 kmph (because they walk in the same direction) distance = 10.5 km time = distance / speed=10.5/1.5=7 hr Answer :C The answer is: C
C
mathematics
Car A runs at the speed of 58km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
[ "11 : 6", "12 : 7", "29 : 18", "15 : 6", "13 : 6" ]
Sol. Distance travelled by Car A = 58 × 8 = 464 km Distance travelled by Car B = 70 × 4 = 280 km Ratio = 464/280 = 29 : 18 C The answer is: C
C
mathematics
Here is a list of names with numbers assigned to them Lavesh = 622 Anmol = 522 Shruti = 620 Aakriti = 742 Based on above Logic what is the value of Sonal ?
[ "522", "422", "624", "570", "750" ]
A 1st Number = Number of alphabtes 2nd Number = Number of vowels 3rd Nummber = Number Of Circles Lavesh = 6 alphabets + 2 vowels(a,e) + 2 circles(in 'a' and in 'e') = 622 Anmol = 5 alphabets + 2 vowels(a,0) + 2 circles(in 'a' and in 'e') = 522 Shruti = 6 alphabets + 2 vowels(u,i) + 0 circles = 620 Aakriti = 7 alphabets + 4 vowels(a,a,i,i) + 2 circles(in 'A' and in 'a') = 742 Hence, Sonal = 5 alphabets + 2 vowels(a,o) + 2 circles(in 'a' and in 'o') = 522 The answer is: A
A
mathematics
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 17 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
[ "40", "50", "60", "68", "None of these" ]
E+H+G+M/4−E+S+M+H/4=17 ⇒ G - S = 68 Answer D The answer is: D
D
mathematics
List L: ABC, BCA, CAB In list L above, there are 2 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
[ "47", "114", "152", "161", "488" ]
Let's try to sum the 2 given numbers taking their place values into account: (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 100(A + B + C) + 10(A + B + C) + (A + B + C) = 111*(A + B + C) We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152 Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases. Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3 A, B and C are all even. 2+4+8 = 14. Factors 2 and 7 Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get. D The answer is: D
D
mathematics
Alice picked a number of pears, each of which she sold, canned, or poached. She canned 20 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 42 pears, then how many pears did she sell?
[ "20", "21", "22", "23", "24" ]
Let x be the amount of pears that she sold. Then she poached 0.5x. Then she canned 1.2*0.5x=0.6x. The total amount of pears is x+0.5x+0.6x=2.1x The fraction of pears that she sold is 1/2.1=10/21. The number of pears she sold is (10/21)*42=20. The answer is A. The answer is: A
A
mathematics
If (x/y)=(6/5), find the value (x^2+y^2)/(x^2-y^2)
[ "61/11", "51/11", "41/11", "21/11", "None of them" ]
= (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(6/5)^2+1] / [(6/5)^2-1] = [(36/25)+1] / [(36/25)-1] = (61*25)/(25*11) = 61/11 Answer is A. The answer is: A
A
mathematics
In a 100-mile trip, the first 30 miles were completed at 60 mph. If the average speed for the whole trip was 40 mph, what was the average speed in the last 70 miles?
[ "30 mph", "32 mph", "35 mph", "37 mph", "38 mph" ]
The time to complete the first 30 miles was (30 miles / 60 mph) = (1/2) hours. The time to complete the whole trip was (100 miles / 40 mph) = (5/2) hours. The time to complete the last 70 miles was (5/2) - (1/2) = (2) hours. The average speed in the last 70 miles was (70 miles / 2 hours) = 35 mph. The answer is C. The answer is: C
C
mathematics
Two friends are training for a marathon together. Billie is faster than Joey, so they agree to giving Joey a half-hour head start, Joey leaving their warm up at 1:30. Joey runs a 3 minute mile (an average of 20 mph), and Billie runs at an average of 50 mph. When will Billie catch up to Joey?
[ "3:00", "3:30", "4:00", "4:30", "5:00" ]
Distance covered by the Joey in 1/2 hour = 20 miles Now, 10 miles is compensated in 1 hour Therefore 20 miles will be compensated in 2 hours So, Billie meets Joey at 4 p.m. Correct Answer: C The answer is: C
C
mathematics
1397 x 1397 = ?
[ "1961609", "1851609", "1951619", "1951609", "1851619" ]
1397 x 1397 = (1397)^2 = (1400 - 3)^2 = (1400)^2 + (3)^2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer is D. The answer is: D
D
mathematics
A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
[ "476 m", "420 m", "440 m", "407 m", "402 m" ]
Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 48 = 15 x + 300 = 720 x =420 m. Answer: B The answer is: B
B
mathematics
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 65 sq. cm. Find the length of the rectangle.
[ "12cm", "14cm", "16cm", "18cm", "20cm" ]
Explanation: Let breadth = x. Then, length = 2x. Then, (2x - 5) (x + 5) - 2x * x = 65 => 5x - 25 = 65 => x = 16. Length of the rectangle = 16 cm. Answer: Option C The answer is: C
C
mathematics
A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
[ "145", "155", "165", "175", "185" ]
The number of ways to form a group of 3 is 12C3 = 220 The number of groups with no senior partner is 7C3 = 35 The number of groups with at least one senior partner is 220-35 = 185 The answer is E. The answer is: E
E
mathematics
If the price of 23 balls is 276, then what will the price of 12 balls?
[ "144", "148", "156", "186", "None of these" ]
Explanation : Less balls, Less Price (Direct Proportion) So, let the price be Rs. x then, 23:12::276:x =>x=276*12/23 =>x=144 So price of 12 balls will be Rs. 144 Answer : A The answer is: A
A
mathematics
By selling 95 pens, a trader gains the cost of 19 pens. Find his gain percentage?
[ "20%", "21%", "22%", "23%", "24%" ]
Let the CP of each pen be Rs. 1. CP of 95 pens = Rs. 95 Profit = Cost of 19 pens = Rs. 19 Profit% = 19/95 * 100 = 20% Answer:A The answer is: A
A
mathematics
A pair of articles was bought for $50 at a discount of 50%. What must be the marked price of each of the article?
[ "$25", "$12.50", "$29.65", "$35.95", "$45.62" ]
S.P. of each of the article = 50/2 = $25 Let M.P = $x 50% of x = 25 x = 25*.5 =$12.50 Answer is B The answer is: B
B
mathematics
If 28a+30b+31c=427. then a+b+c=?.a,b,c are natural numbers
[ "6", "14", "12", "45", "28" ]
have a look on your calender since,we all knw a year consist of 365 days february is d only month which has 28 days 4 months in a year has 30 days and,rest 7 months has 31 days.. so,following d given eq. we can write 28*1 + 30*4 + 31*9.. hence values of a,b and c are 1, 4 and 9 respectively.. a+b+c=14 ANSWER:B The answer is: B
B
mathematics
How many positive, 3-digit integers contain at least one 7?
[ "171", "200", "243", "252", "271" ]
Contains only one 7: 7XX: 1*9*9 = 81 X7X: 8*1*9 = 72 XX7: 8*9*1 = 72 Contains two 7s: 77X: 1*1*9=9 X77: 8*1*1 = 8 Contains three 7s: 777: 1 Total 243 ANS:C The answer is: C
C
mathematics
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
[ "80/9 sec", "80/7 sec", "30/7 sec", "80/8 sec", "81/7 sec" ]
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps. The time required = d/s = (100 + 100 + 200)/35 = 400/35 = 80/7 sec.Answer:B The answer is: B
B
mathematics
How many multiples of 8 are less than 7600, and also multiples of 19?
[ "104", "100", "50", "89", "90" ]
LCM of 8 & 19 = 152 Tried dividing 7600 by 152 Got quotient 50'So C is answer The answer is: C
C
mathematics
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 10 p.c?
[ "38028", "38000", "32977", "38128", "36000" ]
CP + CP/8 = 45000 CP = 40000 SP = 40000*(90/100) = 36000 Answer:E The answer is: E
E
mathematics
The average of nine numbers is 15. The average of first four numbers is 11 and the average of last four numbers is 14. What is the middle number?
[ "19", "20", "35", "31", "27" ]
The total of nine numbers = 9X15 = 135 The total of first 4 and last 4 numbers is = 4 X 11+4 X 14 = 100 So, the middle number is (135 - 100 ) = 35 C The answer is: C
C
mathematics
How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?
[ "8", "12", "60", "118", "120" ]
ways in which 3 seats out 5 can be selected = 5C3 ways in which 3 people can be arranged in 3 seats = 3! Total ways of arrangement = 5C3*3! =5*4/2*6 =10*6 =60 Ans = C The answer is: C
C
mathematics
The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 12 homes?
[ "$200,000", "$210,000", "$215,000", "$220,000", "$230,000" ]
IMO the answer has to be D. 5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 12 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 12x=120,000. x=10,000. The 12 houses are sold at $10,000 profit or at $210,000. (ANSWER B) The answer is: B
B
mathematics
one man can do a piece of work in 10days. one boys join him & he complete the work in 6days . if he gets 50rs for his work then what will be the share of the boy.
[ "10", "20", "30", "40", "50" ]
1 day work of Man=1/10, If Boy's 1 day work=1/x, then (1/10)+(1/x)=1/6, x=15 Ratio of work of Man & Boy=1/10:1/15=3:2 So out of 50 Rs. Boy's share=2*50/(3+2)=20 ANSWER:B The answer is: B
B
mathematics
On a baseball team, 6 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?
[ "1/4", "1/3", "1/2", "2/3", "3/4" ]
The total number of ways to choose three players is 6C3=20. Excluding Alice, the number of ways to choose three players is 5C3=10. P(Alice is not chosen)=10/20=1/2. P(Alice is chosen)=1 - 1/2 = 1/2. The answer is C. The answer is: C
C
mathematics
Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 5000 Km?
[ "10.", "250.", "30.", "38.", "50." ]
Total distance= Distance travelled by A +Distance travelled by car B Distance= speed*time Distance of A= 3x * 6 Distance of B= x*2 (3x * 6) + (x*2) = 5000 x= 250 KM/hr B is the answer The answer is: B
B