divelab/Sys2Bench huggingface dataset:
Question: The y intercept of a line L is 10. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
Options:
A)I only
B)II only
C)III only
D)I and II
E)I and III
Rationale: C) III only
The y-intercept is 10. Therefore we have y=mx+10
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out III.
If you choose to go with the options directly, here's an approach.
y=mx+10. For the x-intercept, y=0.
i.e. mx+10=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+10 =0 would never be satisfied.
If x=6, we have 6m+10=0. A value of m=-5/3 would satisfy this equation.(ANSWER C)
Answer: C
Question: Mr. Jones sold two pipes at $1.20 each. based on the cost , his profit one was 20% and his loss on the other was 20%. on the sale of the pipes, he:
Options:
A)broke even
B)lost 4 cents
C)gained 4 cents
D)lost 10 cents
E)gained 10 cnets
Rationale: 20%profit on $1.20=$20/100x1.20, =$0.20x1.20, = $0.24, similarly , 20 %loss on $1.20, =$20/100x1.20, =$0.20x1.20, =$0.24, therefoe, in one pipe his profit is $ 0.24 and in the other pipe his loss is $0.24. answer: broke even.correct answer will be (A)
Answer: A
Question: A shipping company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options:
A)16
B)64
C)256
D)576
E)4096
Rationale: Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: C
Question: By selling an article at Rs.250, a profit of 25% is made. Find its cost price?
Options:
A)s.486
B)s.455
C)s.220
D)s.480
E)s.200
Rationale: SP = 250
CP = (SP)*[100/(100+P)]
= 250* [100/(100+25)]
= 250* [100/125]
= Rs.200
Answer: E
Answer: E
Question: The side of a rhombus is 22 m and length of one of its diagonals is 16 m. The area of the rhombus is?
Options:
A)327.9
B)325.9
C)347.7
D)357.9
E)327.9
Rationale: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 22 ; p = 16
A=1/2 * 16 *√4(22)2 - (16)2
=1/2 * 16 *√1936 - 256
=1/2 * 16 *√1680
A =327.9
Answer : A
Answer: A
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 40,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
Options:
A)70,000
B)112,000
C)80,000
D)90,000
E)10,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 40, 000km = 112,000 km. B
Answer: B
Question: A and B can together finish a work in 30days. They worked together for 20days and then B left. After another 20days, A finished the remaining work. In how many days A alone can finish the job?
Options:
A)20
B)30
C)60
D)50
E)80
Rationale: A+B 20days work = 20*1/30 = 2/3
Remaining work = 1-2/3 = 1/3
1/3 work is done by A in 20days
whole work will be done by A in 20*3 = 60days
Answer is C
Answer: C
Question: A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?
Options:
A)450 lines
B)200 lines
C)350 lines
D)250 lines
E)150 lines
Rationale: 5-think
5-type
5-break
5-type
5-think
5-break
5-type
5-type
5-break
5-think
5-type
5-break
so 5 times for 5 minutes SE types.
Total number of lines =250 lines
ANSWER:D
Answer: D
Question: Set X consists of 10 integers and has median of 30 and a range of 20. What is the value of the greatest possible integer that can be present in the set?
Options:
A)32
B)37
C)C.40
D)43
E)50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20, 20, 20, 20, 20, 50
This is possible. Hence it is the greatest such number.
Answer (E)
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
Options:
A)2288
B)276
C)800
D)288
E)277
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer:C
Answer: C
Question: A jogger running at 9 km/hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)67 sec
B)89 sec
C)38 sec
D)87 sec
E)45 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 260 + 120 = 380 m.
Time taken = 380/10
=38 sec.
Answer: C
Answer: C
Question: Joel sailed for 3 hours at a speed of 20 miles per hour, then for 6 hours at 30 miles per hour and finally, 1 more hour at 40 miles per hour. What was the average speed of Joel during the whole sail?
.
Options:
A)25
B)27.5
C)28
D)30
E)32
Rationale: 3 hours at a speed of 20 miles per hour gives us Distance = 20*3 = 60 miles
6 hours at a speed of 30 miles per hour gives us Distance = 30*6 = 180 miles
1 more hour at 40 miles per hour gives us Distance = 40*1 = 40 miles
Total Distance = 60+180+40 = 280 miles
Total Time = 3+6+1 = 10 Hours
Average Speed = 280 / 10 = 28 Miles per hour
ANSWER:C
Answer: C
Question: A student must answer 7 out of 10 questions on an competitive examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
Options:
A)90
B)80
C)70
D)100
E)110
Rationale: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
E
Answer: E
Question: A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.4 per box per month for the record storage, what is the total amount that the company pays each month for record storage?
Options:
A)a. 150
B)b. 300
C)c. 600
D)d. 240
E)e. 200
Rationale: Volume Per Box: 15x12x10 = 1,800
Total Volume: 1,080,000
Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600
Price Per Month: Number of Boxes * Price Per Box = 600 * 0.4 = 240
Answer: D
Answer: D
Question: In an encryption code 'HOUSE' is written as '1S902' when encoded and 'DASH' is written as '4G01' when encoded. How is ''SHED" written in that encryption code?
Options:
A)S109
B)0SG1
C)0124
D)G910
E)102G
Rationale: 0 = S
1 = H
2 = E
4 = D
Answer: Option C
Answer: C
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)18 sec
B)17 sec
C)14 sec
D)10 sec
E)11 sec
Rationale: A
D
RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: D
Question: Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
Options:
A)20/7
B)4/3
C)15/8
D)9/4
E)15/4
Rationale: (1/2 + 1/5)t=2
t=20/7
Answer: A
Answer: A
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 6, what is the units digit of (a+2)^2?
Options:
A)1
B)3
C)5
D)6
E)8
Rationale: If the units digit of a^2 is 9, then the units digit of a is either 3 or 7.
If the units digit of (a+1)^2 is 6, then the units digit of a+1 is either 4 or 6.
To satisfy both conditions, the units digit of a must be 3.
Then a+2 has the units digit of 5, thus the units digit of (a+2)^2 will be 5.
The answer is C.
Answer: C
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does
the wheel move in one hour?
Options:
A)6 metre
B)12 metre
C)120 metre
D)1200 metre
E)2200 metre
Rationale: Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *20) cms = 12000 cms
In metres = 120 metre
Answer: C
Answer: C
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be
Options:
A)Rs.169.50
B)Rs.1700
C)Rs. 175.50
D)Rs. 180
E)None
Rationale: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-153/22.50 = 1 =› x - 153 = 22.50 =› x=175.50.
Hence, price of the third variety = Rs.175.50 per kg.
Answer C
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)276 m
B)167 m
C)245 metrs
D)167 m
E)178 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer:C
Answer: C
Question: A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among five colors produced enough color codes to identify all but 6 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: 5C2 = 10
The number of test subjects is 10 + 6 = 16
The answer is C.
Answer: C
Question: n a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
Options:
A)2 hrs
B)3 hrs
C)1 hr
D)4 hrs
E)5 hrs
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
ANSWER C
Answer: C
Question: Shepherd Gopal had a curious aptitude for mathematics and he was known around where he lived as the 'Counting Shepherd.
A man passing throughthe meadow one dat saw Gopal grazing a number of sheep and in the course of a short conversation asked him how many of the grazing sheep were his own. Gopal's reply absolutely baffled him, which was as follows:
If you divide my sheep into two different parts, the difference between yhe two numbers will be the same as the difference between their squares. Now figure it out for yourself the number of sheep I own.'
Can you say just how many sheep Gopal had?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: A
Shepherd Gopal had one sheep only.
Answer: A
Question: A train 120 meters long completely crosses a 480 meters long bridge in 55 seconds. What is the speed of the train is?
Options:
A)32
B)545
C)39
D)40
E)09
Rationale: S = (120 + 480)/45 = 600/55 * 18/5 = 39
Answer: C
Answer: C
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Options:
A)2.04%
B)6.12%
C)8%
D)8.25%
E)10%
Rationale: Per quarter, interest = 2%
So for a year, interest = 8%
Due to quarter cumulation, effective yield (YTM) would be slight higher than 8%
Answer = 8.25% =ANSWER:D
Answer: D
Question: What is the ratio between perimeters of two squares one having 2 times the diagonal then the other?
Options:
A)3: 8
B)3: 6
C)3: 7
D)2: 1
E)3: 3
Rationale: d = 2d d = d
a√2 = 2d a√2 = d
a = 2d/√2 a = d/√2 => 2: 1
Answer:D
Answer: D
Question: A train passes through a telegraph post in 9 seconds moving with a speed of 54 km per hour. The length of the train is
Options:
A)135 metres
B)145 metres
C)125 metres
D)155 metres
E)None of these
Rationale: We know from the formula Distance = Speed x time
Thus, Distance = 54 x 5/18 x 9
or, Distance =135 meters.
ANSWER:A
Answer: A
Question: The total cost of 100 paper plates and 200 paper cups is $4.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
Options:
A)$.80
B)$1.00
C)$1.20
D)$1.50
E)$1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $4.00
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $0.80
Therefore OA is A
Answer: A
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Options:
A)20002
B)20000
C)20007
D)200018
E)20012
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer:B
Answer: B
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 23 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
Options:
A)240 m
B)220 m
C)195 m
D)224 m
E)239 m
Rationale: A
195 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 23)m = 345 m.
Let the length of the platform be x metres.
Then, (x + 345)/36 = 15
--> x + 345 = 540
x = 195m. C
Answer: C
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II, and III
Rationale: Given:
1) a is even prime. The only even prime number known is 2, so a must be equal to 2.
2) a,b,c are consecutive such that a<b<c. So, b must be 3 and c must be 4.
So, we know that a=2, b=3 and c=4.
Substituting the above values in the three equations,
I. abc<a^3
which simplifies to 24<8. False.
II. a+b+c>a^3
which simplifies to 9>8. True.
III. 5b<bc
which simplifies to 15<12. False.
The only option correct is II, so the answer is B.
Answer: B
Question: If X is to be chosen at random from the integers between 1 to 5, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/6
Rationale: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 2/5*2/4 = 1/5
P(X and Y are both odd) = 3/5*2/4 = 3/10
P(X+Y is even) = 1/5 + 3/10 = 1/2
The answer is A.
Answer: A
Question: In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ?
Options:
A)62
B)45
C)28
D)20
E)24
Rationale: a+b+c+d+e=36*5=180
b+c=107
a=x
e=x-8
d=x-3
now 3x-11+107=180
3x=84
x=28
e's score=28-8=20
ANSWER:D
Answer: D
Question: 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?
Options:
A)5.78
B)5.28
C)5.76
D)5.16
E)5.19
Rationale: 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
Answer: C
Question: Nicole cycles at a constant rate of 24 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
Options:
A)x/4
B)x/3
C)x/2
D)x
E)4x/3
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 24 = x/48 hours = 5x/4 minutes
Jessica needs to wait 5x/4 - x = x/4 minutes.
The answer is A.
Answer: A
Question: X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 28 days. How long will Y take to complete the work?
Options:
A)10
B)12
C)15
D)18
E)35
Rationale: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 28 days
Whole work will be done by Y in 28*5/4 = 35 days
Answer is E
Answer: E
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)277
B)237
C)245
D)376
E)368
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 =
25/2
==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: C
Question: Each factor of 220 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 55?
Options:
A)1/16
B)5/42
C)1/8
D)3/16
E)1/4
Rationale: the # of factors 220 has is 12 ;
so out of 12 factors only three are multiples of 55: 55, 110 and 220, itself;
So, the probability is 3/12=1/4.
Answer: E.
Answer: E
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 3:2:5 and 4:5:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
Options:
A)41:81:37
B)33:91:81
C)17:28:27
D)38:37:45
E)41:86:89
Rationale: Let the weight of the two alloys be w each
Required ratio =
(3w/10 +4w/12): ( 2w/10+5w/12 ): (5w/10+3w/12)
= 38w/60 : 37w/60 : 45w/60
= 38:37:45
ANSWER:D
Answer: D
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)76 sec
B)16 sec
C)48 sec
D)17 sec
E)54 sec
Rationale: Relative speed
= 60 + 90
= 150 km/hr.
= 150 * 5/18
= 125/3 m/sec.
Distance covered
= 1.10 + 0.9
= 2 km = 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer: C
Answer: C
Question: What is the leastvalue of x.So that 23X57 is divisible by 3?
Options:
A)1
B)3
C)5
D)6
E)8
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
A
Answer: A
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Options:
A)17
B)19
C)20
D)21
E)18
Rationale: C
20
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.
Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage = (14/70 x 100)% = 20%.
Answer: C
Question: if the annual rate of simple interest increases from 10% to 12.5% .Then a man’s yearly income from an investment increases by Rs.1250. His principle amount is:
Options:
A)Rs,45000
B)Rs.50,000
C)Rs. 60,000
D)Rs.65,000
E)Rs.75,000
Rationale: Let the sum be Rs.x Then, (x*25/2*1/100) – (x*10*1/100)= 1250
25x-20x = 250000 ;
x=50000
ANSWER:B
Answer: B
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/7%
B)33 1/6%
C)33 1/3%
D)38 1/3%
E)33 2/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: C
Question: A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)298 m
B)268 m
C)700 m
D)267 m
E)181 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (600 + x)/60 = 65/3
x = 700 m.
Answer: C
Answer: C
Question: If 213 × 16 = 3408, then 0.16 × 2.13 is equal to :
Options:
A)0.3408
B)3.408
C)34.08
D)340.8
E)None of these
Rationale: Solution
0.16 × 2.13 = (16/100x 213/100)= (16x 213/10000) = 3408/10000 = 0.3408. Answer A
Answer: A
Question: Which of the following is a parallelogram:-
Options:
A)130,50,130,50(angle in deg)
B)120,30,130,20(angle in deg)
C)90,90,90,90(angle in deg)
D)a & c
E)none
Rationale: sum of adjacent angles is 180 degrees.
so, a&c
ANSWER:D
Answer: D
Question: Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
A)3/140
B)1/280
C)3/280
D)3/35
E)68/280
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 68/280.
Answer: E.
Answer: E
Question: The cost of 8 pens and 4 pencils is Rs.200and the cost of 2pens and 2 pencils is Rs.48. Find the cost of each pen?
Options:
A)Rs.32
B)Rs.36
C)Rs.42
D)Rs.26
E)Rs.104
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
8p + 4q = 200 --- (1)
2p + 2q = 48
4p + 4q = 96 --- (2)
(1) - (2) => 4p = 104
=> p = 26
ANSWER:D
Answer: D
Question: If a function f is defined by f(x)= 1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 3/2 then b= ?
Options:
A)-3
B)1/3
C)-1/3
D)3
E)-12
Rationale: Given that f(x) = 1/x and f(a) = -1/2, then f(a) =1/a=-1/2 ===> a=-2, then backsolve using the answer choices:
f(ab) = f(-2b) = 1/6
A) -3 ===> f(-2*-3) = f(6) = 1/6
B) 1/3 ===> f((-2*1/3) = f(-2/3) = 1/(-2/3) = -3/2
C) -1/3 ===> f(-2*-1/3) = f(2/3) = 1/(2/3) = 3/2 WINS
D) 3 ===> f(-2*3) = f(-6) = -1/6
E) -12 ===> f(-2*-12) = f(24) = 1/-24 = -1/24
Answer: C
Answer: C
Question: If n = (32)^43 + (43)^33 what is the units digit of n?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: First of all, the units digit of (32)^43 is the same as that of 3^43 and the units digit of (43)^33 is the same as that of 3^33. So, we need to find the units digit of 3^43 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:
3^1=3 (the units digit is 3)
3^2=9 (the units digit is 9)
3^3=27 (the units digit is 7)
3^4=81 (the units digit is 1)
3^5=243 (the units digit is 3 again!)
...
Thus:
The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).
The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (23)^43 + (43)^33 is 5 + 3 = 0.
Answer: E.
Answer: E
Question: A man took a loan from a bank at the rate of 12% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
Options:
A)Rs. 2000
B)Rs. 10,000
C)Rs. 15,000
D)Rs. 20,000
E)None
Rationale: Solution
Principal = Rs.(100x5400/12x3)= Rs. 15000.
Answer C
Answer: C
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Options:
A)2999
B)2788
C)4400
D)2999
E)2989
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
Answer: C
Answer: C