divelab/Sys2Bench huggingface dataset:
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
A)$21.25m
B)$25.5m
C)$106.25m
D)$127.5m
E)$150m
Rationale: 2/10*1/6*(total) = 5
1/30*(total) = 5
(total) = 5*30 = 150
Answer: E.
Answer: E
Question: When 10 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
Options:
A)3 : 4
B)4 : 1
C)3 : 2
D)Data inadequate
E)None of these
Rationale: Let the first and the second numbers be x and y respect then
y + 10% of x = 140% of y
or, y + 0.1x = 1.4y
or, 0.1x = 0.4y
∴ x : y = 0.4 : 0.1 = 4 : 1
Answer B
Answer: B
Question: If a train, travelling at a speed of 270 kmph, crosses a pole in 5 sec, then the length of train is?
Options:
A)281 m
B)325 m
C)117 m
D)375 m
E)350 m
Rationale: D
D = 270 * 5/18 * 5 = 375 m
Answer: D
Question: Difference between two numbers is 6, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)5,6
B)7,9
C)9,15
D)11,12
E)13,14
Rationale: Explanation:
x – y = 6
4x – 6y = 6
x = 15 y = 9
C)
Answer: C
Question: If r and y are integers, then ry(r + y) is
Options:
A)Always positive
B)Always negative
C)Positive when r is positive
D)Negative when r is negative
E)It cannot be determined by the information given
Rationale: Given r and y are integers, then ry(r + y)
Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..
I presume its Option E if am not missing anything.
r=-3 and y=1
ry(r + y) is positive = 6
Answer: E
Question: What number has a 20:1 ratio to the number 10?
Options:
A)130
B)100
C)200
D)150
E)120
Rationale: 20:1 = x: 10
x = 10*20
x=150
ANSWER:C
Answer: C
Question: How many terms are there in 2,4,8,16,………..1024?
Options:
A)10
B)6
C)9
D)8
E)7
Rationale: Let the number of terms be n. Then,
2 * 2 ^n – 1 = 1024 ,
2^ n-1 = 512 = 2^ 9
n – 1 = 9, n = 10
ANSWER:A
Answer: A
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $174, how many hours overtime did he work?
Options:
A)8
B)5
C)9
D)6
E)10
Rationale: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $174 - $120 = $54 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $54/$6 = 9
Ans is C
Answer: C
Question: If x > 0.8, which of the following could be the value of x?
Options:
A)√0.03
B)√0.8
C)√0.07
D)√0.06
E)√0.05
Rationale: Answer : B
Answer: B
Question: The average age of 15 men of a group is 17 years. Out of these, the average age of 5 men is 14 years and that of the other 9 men is 16 years. The age of the 15th man is?
Options:
A)11 years
B)17 years
C)41 years
D)14 years
E)12 years
Rationale: Age of the 15th student
=[15 * 17 - (14 * 5 + 16 * 9)]
= (255 - 214)
= 41 years.
Answer:C
Answer: C
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
Options:
A)288
B)528
C)299
D)277
E)200
Rationale: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
x = 528
Answer: B
Answer: B
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)22
B)30
C)99
D)88
E)11
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: B
Answer: B
Question: If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. b - a = 1
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
Options:
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then b = a + 1, from which it follows that b - a = 1. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: E.
Answer: E
Question: If 20 honey bees make 20 grams of honey in 20 days, then 1 honey bee will make 1 gram of honey in how many days?
Options:
A)1
B)3.5
C)20
D)49
E)30
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 20 :: 20 : x
Honey 20 : 1
=> 1 x 20 x x = 20 x 1 x 20
=> x = 20.
Answer : C
Answer: C
Question: there is a set of 52 card.1 card fall down.then we take 2 cards from the rest.that 2 cards are spade.what is the probablity of that fallen card is spade?
Options:
A)11/50
B)13/50
C)11/20
D)13/20
E)17/50
Rationale: there are total 13 spades card in a pack if we have drawn 2 spade cards from the pack then out of 13 cards only 11 cards are left.
and out 52 card only 50 cards are left in hand.
p(fallen card is spade)=11C1/50C1=11/50
ANSWER:A
Answer: A
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
Options:
A)98%
B)25%
C)29%
D)35%
E)12%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B
Answer: B
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Options:
A)33
B)77
C)24
D)55
E)88
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Answer: C
Question: If $650 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 7 years?
Options:
A)$750.00
B)$823.50
C)$973.25
D)$921.75
E)$110.00
Rationale: Using CI Formula:
A=P(1+r/n)^n*t
A=650(1+5/7)^5*7
A=921.75
Option: D
Answer: D
Question: If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book.
Options:
A)1079
B)1000
C)1100
D)1075
E)None of these
Rationale: Explanation:
Number of digits used in 1 digit numbers = 1*9 = 9
Number of digits used in 2 digit numbers = 2*90 = 180
Number of digits used in 3 digit numbers = 3*900 = 2700
Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320
Hence, number of pages with 4 digit number = 320/4 = 80
Total number of pages = 1079
ANSWER: A
Answer: A
Question: A train 441 m long can cross an electric pole in 21 sec and then find the speed of the train?
Options:
A)88 Kmph
B)89 Kmph
C)76 Kmph
D)16 Kmph
E)18 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 441/21
S = 21 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 76 Kmph
Answer: C
Answer: C
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent T of thatbeforeJuly 1 last year?
Options:
A)90%
B)99%
C)100%
D)101%
E)110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before T= [0.9n (1.1x)]/xn= 0.99 or 99%.B
Answer: B
Question: What is the probability of tossing a coin five times and having heads appear at least two times?
Options:
A)1/32
B)1/16
C)15/16
D)13/16
E)7/8
Rationale: If 'n' coins are tossed there will
nc0 outcomes in which n coins will show head
nc1 outcomes in which 1 head will appear
and so on
Here 5 coins are tossed so the total outcomes = 2 ^5 = 32
Outcomes in which at least 2 heads will appear = 32 - 5c0 - 5c1 = 26
Prob at least two heads will appear = 26/32 = 13/16
ANSWER:D
Answer: D
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)5/21
B)5/22
C)5/20
D)5/18
E)5/19
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21
Answer: A
Answer: A
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
Options:
A)1.01%
B)5.01%
C)3.01%
D)2.01%
E)4.01%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
ANSWER:D
Answer: D
Question: There are 100 boxes numbered from 1 to 100. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
Options:
A)4650
B)4750
C)4850
D)4950
E)5050
Rationale: 1 green ball: 100 ways
2 green balls: 99 ways
3 green balls: 98 ways
4 green balls: 97 ways
etc...
95 green balls: 6 ways
96 green balls: 5 ways
97 green balls: 4 ways
98 green balls: 3 ways
99 green balls: 2 ways
100 green balls: 1 way
The total number of ways is 100*101/2=5050
The answer is E.
Answer: E
Question: Playing kick-ball, 6 people are standing in a circle. two standing positions are considered different only when the position of the people are different relative to each other. what is the total number of possible standing positions in the group?
Options:
A)a.5
B)b.10
C)c.24
D)d.32
E)e.120
Rationale: for 6 people seating arrangement around a circular table = (6-1)!
= 4!
= 5*4*3*2*1
=120
OA is E
Answer: E
Question: All prime numbers are odd numbers
Options:
A)True
B)False
C)All of these
D)Cannot be determined
E)None of these
Rationale: Explanation :
2 is even prime number. Answer : Option B
Answer: B
Question: A man can row downstream at 35 kmph and upstream at 25 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)35, 3
B)25, 5
C)35, 4
D)5, 30
E)30, 5
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 35 --- (1)
and x - y = 25 --- (2)
From (1) & (2) 2x = 60 => x = 30, y = 5.
Answer:E
Answer: E
Question: Which of the following values of x do not satisfy the inequality x2 - 3x + 2 > 0 at all ?
Options:
A)1 ≤ x ≤2
B)-1 ≥ x ≥ -2
C)0 ≤ x ≤ 2
D)0 ≥ x ≥ -2
E)None of these
Rationale: Explanation :
On solving x2 - 3x + 2 > 0 , we get ( x - 1 )( x - 2 ) > 0.
That is the roots are x = 1 or x = 2.
The equation assumes a positive value for all values which belong to the interval less than 1 and greater than 2
For x = 1 and x = 2, it becomes zero and for any value of x between 1 and 2 it becomes negative.
Answer : A
Answer: A
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)8
B)6
C)5
D)3
E)1
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer:A
Answer: A
Question: 3, 7, 15, 27, 43, ?
Options:
A)63
B)56
C)74
D)57
E)32
Rationale: The pattern is + 4, + 8, + 12, + 16, +20
Answer : A.
Answer: A
Question: The total number of digits used in numbering the pages of a book having 356 pages is
Options:
A)732
B)990
C)1098
D)960
E)1405
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 257) = (9 + 180 + 771) = 960.
ANSWER:D
Answer: D
Question: 130 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)8 days
B)6 days
C)7 days
D)9 days
E)13 days
Rationale: 1 women's 1 day work = 1/910
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/910 + 10/140) = 1/13
5 women and 10 children will complete the work in 13 days.
Answer: E
Answer: E
Question: Five kilograms of oranges contained 90% of water. If the next day the concentration of water decreased by 10%, what was the new weight of the oranges, in kilograms?
Options:
A) 4.9
B) 4.8
C) 2.5
D) 2
E) 0.2
Rationale: Five kilograms of oranges contained 90% of water. If the next day the concentration of water decreased by 10%, what was the new weight of the oranges, in kilograms?
(A) 4.9
(B) 4.8
(C) 2.5
(D) 2
(E) 0.2
If C is the answer, then the question means that the concentration of water the newt day became 80%.
Out of 5 kilograms 90%, or 4.5 kilograms was water and 0.5 kilograms was non-water.
The next day, after some water evaporated, oranges became 80% water and 20% of non-water, so the next day 0.5 kilograms of non-water composed 20% of oranges, which means that the new weight of the oranges was x*0.2=0.5 --> x=2.5 kilograms.
Answer: C.
Answer: C
Question: In a can, there is a mixture of milk and water in the ratio 3 : 7. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 7. Find the capacity of the can?
Options:
A)16.6
B)44
C)27
D)50
E)56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 3/10 (T - 8)
After adding milk, quantity of milk in the mixture = 4/11 T.
4T/11 - 8 = 3/10(T - 8)
37T = 880- 264 => T = 16.6.
Answer:A
Answer: A
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740?
Options:
A)Rs.1000
B)Rs.1550
C)Rs.1510
D)Rs.1500
E)None of these
Rationale: Explanation:
1740 = P [1 + (5*16/5)/100]
P= 1500
Answer: Option D
Answer: D
Question: A camera lens filter kit containing 5 filters sells for $87.50. If the filters are purchased individually, 2 of them are priced at $16.45 each, 2 at $14.05 each, 1 at $19.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
Options:
A)7%
B)8%
C)9%
D)10%
E)11%
Rationale: Cost of kit = $87.50
If filters are purchased individually - $16.45*2 + $14.05*2 + $19.50 = $80.50
Amount saved = $87.50 - $80.50 = $7
Required %age = ($7/$87.50)*100 = 8%
So, the correct answer is B.
Answer: B
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
Options:
A)120
B)240
C)360
D)480
E)720
Rationale: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want 6C!/2 -> 720/2 = 360
ANS:C) 360
Answer: C
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
Options:
A)8/15
B)7/15
C)2
D)1/15
E)1/10
Rationale: A's 1 day's work =1/15
B's 1 day's work =1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60	.
(A + B)'s 4 day's work =(7/60 x 4)=7/15.
Therefore, Remaining work =(1 -7/15	)=8/15.
Answer: Option A
Answer: A
Question: 9 friends bought a shopping mall for 12 million dollars. If the all businessman have to pay the same amount and none of them have amount smaller than $1, how much money would they have to pay?
Options:
A)11,999,997
B)12,000,000
C)12,000,002
D)12,000,003
E)12,000,004
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 12,000,000 = 12 and 9 is divisible by 9.
Hence, we need to remove 3 to this number for it to be divisible by 9
Correct Option: A
Answer: A
Question: A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed.
Options:
A)4 1/2km/hr
B)5 km/hr
C)5 1/2km/hr
D)6 km/hr
E)none
Rationale: Sol.
Let the speed be x km/hr. Then,
30x-30*14/15x = 10
⇔ 2x = 10
⇔ x = 10/2
= 5 km/hr
Answer B
Answer: B
Question: Nicky and Cristina are running a 200 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
Options:
A)35
B)30
C)45
D)40
E)50
Rationale: The distance traveled by both of them is the same at the time of overtaking.
3(t+12) = 5t
t=18.
Cristina will catch up Nicky in 18 seconds.
So in 18 seconds Cristina would cover = 18*5 = 90 meter.
Now Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds.
B
Answer: B
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ4, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
Options:
A)I only
B)II only
C)III only
D)I , II and III
E)I and II only
Rationale: it can be a combination of 6,8 or 7,7 or 5,9
I choose D as an answer.
Answer: D
Question: Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that
ball is white
Options:
A)1
B)2/3
C)1/3
D)4/3
E)None of these
Rationale: Explanation:
Total cases = 10 + 20 = 30
Favourable cases = 20
So probability = 20/30 = 2/3
Answer: B
Answer: B
Question: Pandi and Rani invested in a business. They earned some profit which they divided in the ratio of 3:2. If Pandi invested Rs.30, 000, the amount invested by Rani is:
Options:
A)Rs. 65,000
B)Rs. 20,000
C)Rs. 80,000
D)Rs. 90,000
E)Rs. 60,000
Rationale: Invested by Rani = 30000/3*2 = 20000
Answer : B
Answer: B
Question: If (5 - x)/(7 + x) = x, what is the value of x^2 + 8x - 5?
Options:
A)-4
B)-3
C)-2
D)-1
E)0
Rationale: (5-x) = x*(7+x)
(5-x) = 7x+x^2
0 = x^2+8x-5
The answer is E.
Answer: E
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students T in the class?
Options:
A)A)10
B)B)12
C)C)15
D)D)20
E)E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: C
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/3 rd
B)2/5 th
C)2/3 rd
D)1/5 th
E)2/5 th
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
ANSWER:A
Answer: A
Question: If p - q = 2 and
p2+q2=26
, find the value of pq.
Options:
A)7
B)8
C)9
D)11
E)10
Rationale: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2pq=26âˆ’4=22
=>pq=11
Option D
Answer: D
Question: A cylinder of height h is 5/6 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
Options:
A)25%
B)50%
C)60%
D)72%
E)100%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 5/6
New cylinder 3/5
So 3/5/5/6 = 3/5 *6/5= 0.72 or 72%.
Answer D
Answer: D
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/6. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
A)116
B)146
C)152
D)162
E)170
Rationale: The probability of survival for each of the first 3 months of life is 1-1/6= 5/6, so of 200 newborn 200*5/6*5/6*5/6=~116 is expected to survive.
Answer: A.
Answer: A
Question: A train passes a station platform in 34 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?
Options:
A)200
B)210
C)240
D)250
E)260
Rationale: 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 / 34 = 15
x + 300 = 510
x = 210 m.
Answer: Option B
Answer: B
Question: If r<0, which of the following must be true?
Options:
A)–100 < r < 100
B)r ≤ –1
C)r ≤ 1
D)r^2 ≥ 1/4
E)–100 < r < 0
Rationale: r is a negative number.
A. –100 < r < 100r can be a negative number less than -100
B. r ≤ –1r can be a fraction, in which case it would be greater than -1
C. r ≤ 1must be true since 1 is positive and r is negative
D. r^2 ≥ 1/4not true if r is a negative fraction like -1/5
E. –100 < r < 0r can be a negative number less than -100=C
Answer: C
Question: What is the solution of the equations x - y = 0.1 and 1(x + y)-1 = 2 ?
Options:
A)x = 0.3, y = -0.2
B)x = 1, y = 0.1
C)x = 2, y = 1.1
D)x = 1.2, y = 0.3
E)None
Rationale: Answer
x - y = 0.1 ...(i)
and 1(x + y)-1=2
⇒ 1/ (x + y) = 2
⇒ 2(x + y) =1
⇒ x + y = 1/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 0.3
and y = -0.2
Correct Option: A
Answer: A