divelab/Sys2Bench huggingface dataset:
Question: y =2x^2 +2bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
Options:
A)256
B)-256
C)-128
D)-64
E)-257
Rationale: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form ofax^2+bx+c=0,
The product of the roots =c/a= 512/2=256 and the sum of the roots =-b/a=-b
256 can be expressed as product of two numbers in the following ways:
1 * 256
2 * 128
4 * 64
8 * 32
16 * 16
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
The least value possible for b is therefore -257.
E
Answer: E
Question: Calculate the share of profit made by 2 business partners, who invested $800 and $1200 respectively in a business if the profit made is $600.
Options:
A)$241,$360
B)$240,$2260
C)$240,$360
D)$230,$360
E)$220,$360
Rationale: A:B = 800:1200
A:B = 2 : 3
A's share = 600*2/5 = $240
B's share = 600*3/5 = $360
Answer is C
Answer: C
Question: What is the average of xx, 2x2x, and 66?
Options:
A)x+2
B)x+3
C)x+2x+2
D)x+4
E)2x+5
Rationale: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or Option C
Answer: C
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 73, what is the value of x?
Options:
A)71
B)75
C)85
D)83
E)82
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 73
x = 71
Answer : A
Answer: A
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :4. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
Options:
A)18 : 35 : 50
B)3 : 10 : 10
C)4 : 8 : 5
D)8 : 35 : 25
E)None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 4x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 5x × 140% :
4x × 125% = 36 : 70 : 50
= 18 : 35 : 25
Answer D
Answer: D
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 539, Krishan has ?
Options:
A)s. 2890
B)s. 2330
C)s. 1190
D)s. 1620
E)s. 3179
Rationale: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 539 : N
&there N = 289 x 539 / 49
= Rs. 3179
Answer :E
Answer: E
Question: Find the Missing Number 1, 5, 13, 25, ?
Options:
A)41
B)44
C)23
D)26
E)29
Rationale: 5-1=4
13-5=8
25-13=12
So,
41-25=16
ans- 41
ANSWER:A
Answer: A
Question: Lucy deposited $62500 in an investment fund that provided 22 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in years, did her investment earn a total interest of $5100?
Options:
A)1/2
B)1/7
C)3
D)6
E)6.1
Rationale: A = P + I = 62500 + 5100 = 67600
67600 = 62500(1 + 22/4*100)^(4t)
t = 1/7 yrs
Answer: B
Answer: B
Question: What is the greatest prime factor of 5^6 - 1?
Options:
A)29
B)31
C)37
D)41
E)43
Rationale: 5^6-1 = (5^3-1)(5^3+1) = 124*126 = 4*31*3*42
The answer is B.
Answer: B
Question: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
Options:
A)2 <= 8x+10 <= 6
B)2 <= 34x+4 <= 6
C)2 <= 3x+4 <= 6
D)2 <= 3465x+4 <= 6
E)2 <= 346x+4 <= 6
Rationale: The key words in the stem are:a singleline segment offinite length
Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.
Answer: C.
Answer: C
Question: In a series of eight football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 8 draws in the series?
Options:
A)24/576
B)125/864
C)1/25
D)1/65536
E)1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 8 draws in 8 matches is (1/4)^8=1/65536.
Answer: D.
Answer: D
Question: The perimeter of a rectangle is equal to the perimeter of aright-angled triangle of height 12 cm. If the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle”
Options:
A)18 cm
B)24 cm
C)22 cm
D)Data inadequate
E)None of these
Rationale: P = 2(l + b) = L + B + h = L + b + 12.
Data inadequate.
Answer D
Answer: D
Question: At a meeting, 25 attendants used a pencil and 15 attendants used a pen. If exactly 20 attendants used only one of the two types of writing tools, how many attendants wrote with both types of writing tools?
Options:
A)10
B)6
C)7
D)4
E)14
Rationale: Say x attendants wrote with both writing tools.
(25 - x) + (15 - x) = 20 --> x = 10.
Answer: A.
Answer: A
Question: A numberais squared and then multiplied by negative 3. The result of this operation E is equal to three times the sum of three timesaand two. What is one possible value ofa?
Options:
A)-3
B)-2
C)1
D)2
E)3
Rationale: E=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: B
Question: There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
Options:
A)7!*3!
B)7!*2!
C)6!*3!
D)5!*2!
E)8!*3!
Rationale: Total number of ways = 7!*2!.
B
Answer: B
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)28
B)26
C)25
D)21
E)20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer:E
Answer: E
Question: Two stations A and B are 65 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)9
B)10
C)11
D)12
E)8
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 65
45x = 90
x = 2.
So, they meet at 9 a.m.
Answer: Option A
Answer: A
Question: A completes a work in 6 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be
Options:
A)8 days
B)9 days
C)10 days
D)12 days
E)4 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 6 × 12/ 18 = 4days.
Answer : E
Answer: E
Question: If the population of a certain country increases at the rate of Two person every 60 seconds, by how many persons does the population increase in 100 minutes?
Options:
A)120
B)150
C)240
D)220
E)200
Rationale: Answer = 2 * 100 = 200
Answer = E
Answer: E
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Options:
A)49
B)4
C)12
D)9
E)27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x 14 * x = 6 x 21
x =	(6 x 21)/14
x = 9.
Answer is D.
Answer: D
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Options:
A)10
B)19
C)20
D)25
E)17
Rationale: Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years.
Required average = 57/3 = 19 years.
ANSWER B
Answer: B
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 2 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Options:
A)396
B)1260
C)2475
D)7920
E)15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 2 and 11..ie., 10 possible numbers
Possible combinations for X1,X2 would be 10C2 = 45
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 45 * 55 = 2475
Ans. C
Answer: C
Question: The average monthly income of P and Q is Rs. 2050. The average monthly income of Q and R is Rs. 5250 and the average monthly income of P and R is Rs. 6200. The monthly income of P is:
Options:
A)3050
B)3000
C)4000
D)4050
E)3100
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (2050 x 2) = 4100 .... (i)
Q + R = (5250 x 2) = 10500 .... (ii)
P + R = (6200 x 2) = 12400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 27000 or P + Q + R = 13500 .... (iv)
Subtracting (ii) from (iv), we get P = 3000.
P's monthly income = Rs. 3000.
Answer: B
Answer: B
Question: The number which exceeds 16% of it by 42 is?
Options:
A)50
B)25
C)52
D)58
E)60
Rationale: Let the number be x.
Then, x - 16% of x = 42.
x - 16/100 x = 42
x = (42 * 25)/21 = 50
ANSWER:A
Answer: A
Question: Rs.1430 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)s.528
B)s.542
C)s.528
D)s.540
E)s.660
Rationale: A+B+C = 1430
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1430 = Rs.660
Answer: E
Answer: E
Question: There are 5 more women than there are men on a local co-ed softball team. If there are a total of 15 players on the team, what is the ratio of men to women?
Options:
A)10/16
B)6/16
C)5/10
D)6/10
E)4/10
Rationale: w = m+5
w+m = 15
m+5+m = 15
2m = 10
m = 5
w = 10
ratio:5:10
Ans: C
Answer: C
Question: In how many ways 8 different tickets R can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
Options:
A)From 2 to 6 inclusive.
B)From 98 to 102 inclusive.
C)From 122 to 126 inclusive.
D)From 128 to 132 inclusive.
E)From 196 to 200 inclusive.
Rationale: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
R=1+28+70+28+1 = 128 Answer is D.
Answer: D
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 1200. Their H.C.F is?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x = 1200
x = 20
The numbers are 3*20 , 4*20 , 5*20
Hence required H.C.F. = 20
Answer is A
Answer: A
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Options:
A)4208
B)4202
C)4209
D)4200
E)42012
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer: D
Answer: D
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 3w widgets.
Options:
A)4
B)6
C)18
D)10
E)12
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 18 days to doing 3w widgets.
Answer : C
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)17 km/hr
B)88 km/hr
C)36 km/hr
D)99 km/hr
E)45 km/hr
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Answer: C
Question: An event manager has ten patterns of chairs and eight patterns of tables. In how many chairs can he make a pair of table and chair?
Options:
A)100
B)120
C)60
D)80
E)90
Rationale: He has 10 patterns of chairs and 8 patterns of tables.
Hence,A chair can be arranged in 10 ways
A table can be arranged in 8 ways
Hence one chair and one table can be arranged=10*8 ways
=80 ways
Option D
Answer: D
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 120 marks, the no of questions he attempts correctly is :
Options:
A)35
B)36
C)40
D)42
E)44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 120
=> 5x = 180
=> x = 36
Answer: B
Answer: B
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts W needed to confirm that each of the 5 keys matches each of the 5 locks?
Options:
A)5,15
B)4,15
C)5,10
D)4,10
E)5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of W= 4 + 3 + 2 + 1 = 10 attempts.D
Answer: D
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 17000, then find the annual income of A?
Options:
A)Rs. 571200
B)Rs. 180000
C)Rs. 201600
D)Rs. 504000
E)None of these
Rationale: B's monthly income = 17000 * 112/100 = Rs. 19040
B's monthly income = 2 parts ----> Rs. 19040
A's monthly income = 5 parts = 5/2 * 19040 = Rs. 47600
A's annual income = Rs. 47600 * 12 = Rs. 571200
ANSWER:A
Answer: A
Question: Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?
Options:
A)700
B)710
C)720
D)740
E)750
Rationale: We have to arrange 6 books.
The number of permutations of n objects isn!=n.(n−1).(n−2)...2.1n!=n.(n−1).(n−2)...2.1
Here n=6n=6 and therefore, number of permutations is 6.5.4.3.2.1=6.5.4.3.2.1= 720
Option is C
Answer: C
Question: After the recall of defective by Telvin inc 2 years ago, its share price has since lost 12%. However, after the launch of its new product 1 year ago its stock price has appreciated by 6%, bringing its share price to $25. What was its share price 2 years ago?
Options:
A)28
B)26.8
C)56.6
D)27.2
E)25.7
Rationale: -12+6-(12*6)/100=-6.72% net decrease
let initial price be Y
Y(1-6.72/100)=25
Y=25/0.9328 = ~26.8
Ans is B)
Answer: B
Question: A "word" is defined as a sequence of three dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
Options:
A)3
B)5
C)6
D)8
E)9
Rationale: there are two ways of possibilities..
1) all three same colour- YYY or BBB- 2 ways
2) two of one colour and one of different colour- 3!/2!-3ways..
now two /one could be Y/B or B/Y.... so 3*2=6..
total 6+2=8 ans D
Answer: D
Question: Which of the following is the lowest positive integer that is divisible by the first 8 positive integer multiples of 3?
Options:
A)1720
B)2120
C)2520
D)2920
E)3320
Rationale: The number must be divisible by 3, 2*3, 3^2, 2^2*3, 5*3, 2*3^2, 7*3, and 2^3*3.
The lowest such number is 2^3*3^2*5*7 = 2520.
The answer is C.
Answer: C
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2998
C)2778
D)2788
E)2991
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: A
Question: A pupil's marks were wrongly entered as 83 instead of 53. Due to the average marks for the class got increased by half. The number of pupils in the class is?
Options:
A)18
B)82
C)60
D)27
E)29
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 53) => x/2
= 30 => x = 60.
Answer: C
Answer: C
Question: What comes next in the sequence?
4, 2, 4, 8, 6, 8, 16
Options:
A)14
B)16
C)4
D)18
E)8
Rationale: (4,8,16)
(2,6,18)
(4,8,16)
series is 4,2,4,8,6,8,16,18,16
ANSWER:D
Answer: D
Question: Shelly rows 4m kilometers downstream at 6x kilometers per hour. Then she turns around and rows m/6 kilometers upstream at 2x kilometers per hour. What is Shelly's average rowing speed in kilometers per hour during the entire journey?
Options:
A)50x/9
B)50x/(9m)
C)50/9
D)50m/9
E)50mx/9
Rationale: Total distance covered = 4m + m/6 = 25m/6
Total time taken = 4m/6000x + (m/6)/2000x = 9m/12000x = 3m/4000x
Average speed = Total distance/Total Time taken = (25m/6)/(3m/4000x)
= 50,000x/9 mt/hr
= 50x/9 km/hr
Option A.
Answer: A
Question: 2 pipes can separately fill a tank in 20hrs and 30hrs respectively. Both the pipes are opened tofill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
Options:
A)10 hrs
B)12 hrs
C)16 hrs
D)18 hrs
E)20 hrs
Rationale: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
C
Answer: C
Question: A truck covers a distance of 392 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 70 km more than that travelled by the truck ?
Options:
A)6 hours
B)5 hours
C)7 hours
D)8 hours
E)None
Rationale: Explanation :
Speed of the truck = Distance/time = 392/8 = 49 kmph
Now, speed of car = (speed of truck + 18) kmph = (48 + 18) = 66 kmph
Distance travelled by car = 392 + 70 = 462 km
Time taken by car = Distance/Speed = 462/66 = 7 hours.
Answer – C
Answer: C
Question: If k^2 = n^2, which of the following must be true?
Options:
A)k = m
B)k = -m
C)|k| = |n|
D)k = -|m|
E)k = |m|
Rationale: Solution:
We are given that k^2 = n^2, and we can start by simplifying the equation by taking the square root of both sides.
√k^2 = √n^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√k^2 = √n^2 is |k| = |n|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: C
Answer: C
Question: 36 people attend a party. 7 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?
Options:
A)7
B)6
C)5
D)8
E)9
Rationale: Total people = number of men + number of women
36 = 7 + number of married men + 22
number of married men = 36- 22-7 = 7 men
ANSWER:A
Answer: A
Question: A train 250 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:
Options:
A)95
B)50
C)12
D)13
E)67
Rationale: Speed of the train relative to man = (250/10) m/sec = (25) m/sec. [(25) * (18/5)] km/hr = 90 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.
Answer: Option A
Answer: A
Question: Townville has 100 residents, and 30 of them are females. If half of Townville’s male residents are smokers, and 1/3 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
Options:
A)55
B)65
C)25
D)22
E)21
Rationale: Number of people =100
Females = 30
men = 100-30=70
Half of the men are smoker70/2=35, that means the remaining men 70-35=35 are non smokers.
1/3 females are smoker. i.e 1/3*30 = 10.
30-10=20 females are non smokers
So, total number of non smokers in the town are 35+20 =55
Answer : A
Answer: A
Question: The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:21, then find the ratio of their periods of investments.
Options:
A)2:3:6
B)3:5:6
C)3:2:4
D)2:4:3
E)2:5:3
Rationale: The ratio of investments of A, B and C is 5:6:7.
The ratio of shares of A, B and C is 5:9:21.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (21/7) = 1:3/2:3 = 2:3:6.
ANSWER:A
Answer: A
Question: 23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
Options:
A)22
B)23
C)44
D)45
E)46
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 23.
ANSWER:B
Answer: B
Question: Jaime earned enough money by selling seashells at 35 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
Options:
A)5
B)11
C)17
D)22
E)30
Rationale: Let's TEST Answer D: 22 seashells....
With 22 seashells, Jamie would have 22(35) = 770 cents. This would allow him to buy 14 books for 770 cents total, with no money left over. This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
[Reveal]Spoiler:D
Answer: D
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)28
B)27
C)12
D)99
E)14
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:C
Answer: C
Question: How many ways are there to award a gold, silver and bronze medal to 12 contending teams?
Options:
A)12 x 11 x 10
B)10!/(3!7!)
C)10!/3!
D)360
E)300
Rationale: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 12 ways
if gold medal is given to 1 of the teams then only possible 11 teams can be considered for silver medal. we can do selection in 11 ways
similarly if gold and silver medals are awarded then only remaining 10 teams can be considered for a bronze medal. we can do the selection in 10 ways
Total number of ways to select the 3 possible medal winners = 12 * 11 * 10
Correct answer - A
Answer: A
Question: Points M(5,2) and N(5,8) lie on the xy - plane. What is the midpoint of line segment MN?
Options:
A)(5,0)
B)(0,5)
C)(0, (136^(1/2))/2)
D)(3/2,0)
E)(5,5)
Rationale: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:
• The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.
• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.
So, x=(5+5)/2=5 and y=(2+8)/2=5 --> coordinates of the midpoint are (5, 5).
Answer: E.
Answer: E
Question: Half of 5 percent written as decimal is
Options:
A)5
B)0.025
C)0.015
D)0.005
E)None of these
Rationale: Explanation:
It will be 1/2(5%) = 1/2(5/100) = 5/200 = 0.025
Option B
Answer: B