divelab/Sys2Bench huggingface dataset:
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 30%?
Options:
A)Rs. 28985
B)Rs. 40985
C)Rs. 20985
D)Rs. 21000
E)Rs. 30985
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 30/100 (35000)
x = 27985
35000 - x = 6985
Difference in the cost prices of televisions = Rs. 20985
ANSWER:C
Answer: C
Question: If f(x) = Log(x), then f -1(x) =
Options:
A)10 x
B)-10 -x
C)1 / 10 x
D)x 10
E)NONE
Rationale: Solution
y = Log(x) if and only if
x = 10y
Interchange x and y
y = 10x
Hence
f -1(x) = 10x
Answer A
Answer: A
Question: An aeroplane covers a particular distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hour, it must travel at a speed of
Options:
A)300 kmph
B)720 kmph
C)700 kmph
D)450 kmph
E)500 kmph
Rationale: distance=(240*5) = 1200 km
speed=dist/time
req speed = 1200/(5/3)=>720km/hr
ANSWER B
Answer: B
Question: Machine A takes 100 hours to complete a certain job and starts that job at 6AM. After ten hour of working alone, machine A is joined by machine B and together they complete the job at 6PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?
Options:
A)24.65
B)22.27
C)2.273
D)11.62
E)21.13
Rationale: Let us assume total job = 100 units
A finishes 100 units in 100 hrs(given)
Hence A (working rate)= 1 units /hr
Now Given that A works for 10 hr( so 10 units done) then A and B finish total work in 12 hours. Hence A and B finish 90 units in 2 hours. Of these 1x2=2 units were done by A. Hence B did 88units in 2 hours.
Hence B(working rate)= 44 units /hr
Hence B takes 100/44 = 2.273 hours to complete the job.
Answer C.
Answer: C
Question: A pipe can empty 3/4th of a cistern in 12mins. In 8 mins, what part of the cistern will be empty?
Options:
A)1/2
B)3/7
C)4/9
D)3/8
E)4/7
Rationale: 3/4 ---- 12
? ----- 8 ==> 1/2
A
Answer: A
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 4 years ago?
Options:
A)152460
B)214560
C)145125
D)210000
E)200000
Rationale: population 2 years ago = 176400/(1 + 5/100)^4
Answer is C
Answer: C
Question: Frank is 13 years younger then John. In 5 years John will be twice as old as Frank. How old will Frank be in four years?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Frank is 15 years younger then John --> F+13=J;
In 5 years John will be twice as old as Frank (in 5 year John will be J+5 years old and Frank will be F+5 years old) --> J+5=2*(F+5) --> (F+13)+5=2*(F+5) --> F=8;
In 4 years Frank will be 8+4=12 years old.
Answer: C.
Answer: C
Question: In a certain game there are 7 steps, referred to as step 1, step 2, and so on with the final step being step 7. The steps are played one after the other. In each step a score of 1, 2,3 or 4 is obtained. Mary played the game, getting at least one score of each of 1, 2, 3 and 4 and never getting the same score in consecutive steps. What is the greatest possible score that Mary could have gotten?
Options:
A)20
B)19
C)17
D)18
E)16
Rationale: There are two conditions:
1. Mary got at least one score of each of 1, 2, 3 and 4.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2+4+3 = 18
Answer: D.
Answer: D
Question: A 200 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
Options:
A)210m
B)300m
C)230m
D)240m
E)250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+200/9=500/9
x=300
Ans is 300m
ANSWER:B
Answer: B
Question: A train running at the speed of 54 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)135
B)272
C)278
D)277
E)112
Rationale: Speed = 54*(5/18) m/sec = 15 m/sec
Length of Train (Distance) = Speed * Time
(15) * 9
= 135 meter
Answer: A
Answer: A
Question: From given equation find the value of x: 2x² + 9x − 5
Options:
A)−5
B)-4
C)-3
D)3
E)4
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or −5
A
Answer: A
Question: A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?
Options:
A)10.21 days
B)10.23 days
C)18.25 days
D)10.25 days
E)40.25 days
Rationale: Explanation:
A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.
=> In one day A came complete 1/9th of the task(x/9)
=> In one day B can complete 1/12th of the job.(x/12)
First day x/9th work will be done next day x/12th and so on:
Together A and B can do x/9 + x/12 work.
=>(x/9) + (x/12) = 7/36th work done
In 10 days 35/36th of the work will be done.
On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.
So, 1/36th work will be done in 1/4 days.
=>10.25 days
ANSWER: D
Answer: D
Question: Find the value of (875 233/899) × 899
Options:
A)788658
B)786858
C)788865
D)786588
E)None of them
Rationale: =(875 233/899) × 899
=(786625 + 233)/899 × 899
=786858/899 × 899
=786858
Answer is B.
Answer: B
Question: If c = (1/4)a and b = 7c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c ?
Options:
A)2b
B)3b
C)4b
D)5b
E)12b
Rationale: a = (4)c and b =7c.
The mean = (a + b + c)/3 = (4c + 7c + b)/3 = 4b.
Answer is C
Answer: C
Question: A train of length 230 metres takes 58 seconds to cross a tunnel of length 60 metres. What is the speed of the train in km/hr?
Options:
A)58 km/hr.
B)60 km/hr.
C)30 km/hr.
D)18 km/hr.
E)None
Rationale: Sol.
Speed = [230 + 60 / 58] m/sec = [290 /58 * 18/5] km/hr = 18 km/hr.
Answer D
Answer: D
Question: If x, y, and z are distinct positive prime numbers, then (x^3)(y)(z) has how many different positive factors greater than 1?
Options:
A)a. 8
B)b. 9
C)c. 12
D)d. 15
E)e. 17
Rationale: Let Number is (x^3)(y)(z) = (3^3)(4)(5) = 180
We can write 180 as product of two numbers in following ways
1*180
2*90
3*60
4*45
5*36
6*30
9*20
10*18
12*15 9 cases = 9*2 i.e. 18 factors (including 1)
Factors greater than 1 = 17
Answer: Option E
Answer: E
Question: Two pipes can fill a tank in 18 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
Options:
A)5.25 Hours
B)7.25 Hours
C)8.25 Hours
D)9.25 Hours
E)11.25 Hours
Rationale: In 1 hour it fill 1/18 + 1/12 - 1/20 = 4/45
So fill tank fill up in 45/4 = 11.25 Hours
ANSWER:E
Answer: E
Question: The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)22 kmph
B)20 kmph
C)21 kmph
D)26 kmph
E)28 kmph
Rationale: Speed of the boat in still water = (30+70)/2 = 50 kmph. Speed of the stream
= (70-30)/2
= 20 kmph.
Answer:B
Answer: B
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A)72
B)82
C)97
D)268
E)27
Rationale: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average
= 864/12
= 72.
Answer:A
Answer: A
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Options:
A)500
B)1500
C)2000
D)1220
E)1000
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
so the answer is option C) 2000
Answer: C
Question: 5, 11, 23, 41, 64, _
Options:
A)95
B)96
C)97
D)98
E)99
Rationale: 5+6=11
11+6*2;11+12=23
23+6*3;23+18=41
41+6*4;41+24=65 65+6*5;65+30=95
ANSWER:A
Answer: A
Question: In a family 19 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family?
Options:
A)20
B)31
C)9
D)31
E)21
Rationale: Total people eat veg = only veg + both veg and non veg
Total= 19+12= 31
Answer = B
Answer: B
Question: The traffic lights at 3 different roads change after every 36 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
Options:
A)9:18:36
B)9:42:15
C)10:15:24
D)9:54:12
E)10:01:20
Rationale: LCM of 36,72,108 = 216 = 3mnts 36sec
The lines will change every 3m 36sec
The light will change again after 9:15 AM is = 9:15+0:03:36 = 9:18:36
Answer is A
Answer: A
Question: A cistern is filled by pipe A in 20 hours and the full cistern can be leaked out by an exhaust pipe B in 25 hours. If both the pipes are opened, in what time the cistern is full?
Options:
A)50hrs
B)60hrs
C)70hrs
D)80hrs
E)100hrs
Rationale: time taken to full the cistern=(1/20-1/25)hrs
=1/100
=100hrs
ANSWER:E
Answer: E
Question: What is the greatest value of n such that 24^n is a factor of 24! ?
Options:
A)1
B)2
C)3
D)4
E)8
Rationale: Another way to solve this question :
We know that 18 = 2 *3^2.
Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)
No. of 3s = 18/3 =6/3 =2.
Add the numbers in Bold, you will get total number of 3s = 8.
Hence, total number of 4^2 = 16/2 = 8.
Hence, answer is 8. E
Answer: E
Question: 20 14 8
10 5 10
5 ? 3
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: difference bet 20&14=6 and 14&8=6
10&5=5 and 5&10=5
similarly
5&4=1 and 4&3=1
ans is 4
ANSWER:C
Answer: C
Question: find value for x from given equation ? x + 1 = -3
Options:
A)1
B)x=-4
C)-3
D)-5
E)5
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Answer: B
Question: Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 9 + 3 = ??
Options:
A)11
B)12
C)13
D)14
E)18
Rationale: 11
ANSWER:A
Answer: A
Question: A boat can move upstream at 20 kmph and downstream at 34 kmph, then the speed of the current is?
Options:
A)7
B)6
C)8
D)4
E)2
Rationale: US = 20
DS = 34
M = (34 - 20)/2 = 7 Answer:A
Answer: A
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)Rs.1000
B)Rs.1500
C)Rs.6000
D)Rs.3000
E)Rs.2000
Rationale: Explanation:
Let C.P. be Rs. x.
Then,1920-x/x*100=x-1280/x*100
1920 - x = x - 1280
2x = 3200
x = 1600
Required S.P. = 125% of Rs. 1600 = Rs.(125/100*1600) Rs.2000
ANSWER:E
Answer: E
Question: 13, 35, 57, 79, 911, ?
Options:
A)1145
B)1113
C)1117
D)1110
E)1112
Rationale: The terms are formed by joining together consecutive odd numbers in order. i.e. 1 and 3, 3 and 5, 5 and 7, 7 and 9, 9 and 11,....
Answer : B.
Answer: B
Question: 9 - 3 ÷ 1/3 + 6 = ?
Options:
A)1
B)3
C)6
D)9
E)12
Rationale: 9 - 3 1/3 + 6
=9-3÷1/3+6
=9-(3X3) +6
=9-9+6
=6
CORRECT ANSWER : C
Answer: C
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 6 minutes. How much time will be take to cover a distance of 6 kilometres?
Options:
A)48 min.
B)50 min.
C)66 min.
D)55 min.
E)None of these
Rationale: Rest time = Number of rest Ã— Time for each rest
= 5 Ã— 6 = 30 minutes
Total time to cover 6 km
= (6â„10 Ã— 60)minutes + 30 minutes = 66 minutes
Answer C
Answer: C
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 175kg then find the average weight of all the 7 rounds?
Options:
A)100 kgs
B)88.5 kgs
C)86.5 kgs
D)67.5 kgs
E)88.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 175/7 = 100 kgs
Answer:A
Answer: A
Question: A CAN FINISH A WORK IN 6 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
Options:
A)2
B)5 1/2
C)6
D)8
E)NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (6*1/3)=2 DAYS.
CORRECT OPTION:A
Answer: A
Question: A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 30 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
Options:
A)90
B)60
C)70
D)20
E)10
Rationale: Answer is A.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 30 + 30 + 30 + 30 + 30 + 30
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 400 seniors.
So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 30, then f = 90.
A
Answer: A
Question: Circles X and Y are concentric. If the radius of circle X is four times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
Options:
A)13
B)Pi/3
C)Pi/2
D)15/16
E)8/9
Rationale: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 4a, so area = 9. PI a ^ 2
Area of shaded region = 16PI a^2 - PI a^2 = 15 PI a^2
So, probability = ( 15 PI a^2 ) / (16 PI a^2 )
= 15/16= Answer = D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)178 m
B)168 m
C)120 m
D)168 m
E)178 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Answer: C
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is:
Options:
A)89.25 km/hr.
B)77 km/hr.
C)90.25 km/hr.
D)94.25 km/hr.
E)96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (440/5) = 88
x = (88/8) = 11
Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr.
B
Answer: B
Question: The probability of pulling a black ball out of a glass jar is 1/X. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
Options:
A)1/(XY).
B)X/Y.
C)Y/X.
D)1/(X+Y)
E)1/(X-Y).
Rationale: pulling a black ball out of a glass jar and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass jar = P(a) and Prob of breaking the jar = P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer B.
Answer: B
Question: What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?
Options:
A)64.19
B)64.12
C)40.5
D)64.1
E)64.11
Rationale: S.I. = (1000 * 8 * 4)/100 = Rs. 320
C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5
Difference = (360.5 - 320) = Rs. 40.5
Answer: C
Answer: C
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)18
B)27
C)26
D)12
E)19
Rationale: 2 * 22/7 * 14 * x = 1056
=> x = 12
Answer: D
Answer: D
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 50 as remainder. Find the no. is?
Options:
A)220060
B)145778
C)220050
D)220800
E)220030
Rationale: (555 + 445) * 2 * 110 + 50 = 220000 + 50 = 220050
C
Answer: C
Question: 1,3,6,10,15,?
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: 1 =1
1+2 = 3
3+3 = 6
6+4 = 10
10+5 = 15
15+6 = 21
ANSWER:E
Answer: E
Question: The difference between the simple interest received from two different sources on Rs.1500 for 3 years is Rs.13.50. The difference between their rates of interest is
Options:
A)0.1%
B)0.2%
C)0.3%
D)0.4%
E)0.5%
Rationale: (1500xR1x3)/100-(100xR2x3)/100 =13.50
4500(R1-R2)=1350
R1-R2 = 1350/4500=0.3%
answer : D
Answer: D
Question: B takes 12 more days than A to finish a task. B and A start this task and A leaves the task 12 days before the task is finished. B completes 60% of the overall task. How long would B have taken to finish the task if he had worked independently?
Options:
A)48 days
B)36 days
C)28 days
D)32 days
E)22 days
Rationale: DETAILED SOLUTION
Let us say A and B split their share of the task and started doing their respective shares simultaneously.
Let’s say A takes A days to finish the task. Therefore, B takes A + 12 days to finish the entire task.
A has to finish 40% of the task, since B is doing the rest. So A will only take 2A/5 number of days.
B only has to finish 60% of the task, so B will take (3(A+12)/5) number of days.
But as we know, B starts working along with A and finishes 12 days after A stops working.
So, (3(A+12)/5) = ((2A)/5+12)
3A + 36 = 2A + 60
A = 24; B = 36 days.
Answer choice B
Answer: B
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (4x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer
Options:
A)I only
B)I,II,III NOT TRUE
C)I and II
D)I and III
E)II and III
Rationale: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
4x - is always negative and EVEN
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always EVEN
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 - x) is an odd negative integer
y can be 0 => -x will be positive => III statement is not true
basing on above, only I statement will always be true
answer is B
Answer: B
Question: ake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in
Options:
A)48
B)39
C)37
D)27
E)29
Rationale: Simple one. Let the total work to be done is 48 meters. Now Jake can dig 3 mts, Paul can dig 2 mts a day. Now all of them combined dug in 8 days so per day they dug 48/8 = 6 mts. So Of these 8 mts, Hari capacity is 1 mt.
So he takes 48 /1 = 48 days to complete the digging job.
Answer:A
Answer: A
Question: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 4?
Options:
A)1/2
B)1/3
C)2/3
D)1/4
E)2/5
Rationale: There are 3 ways to get a total sum of 10.
2 of these ways include the number 4.
The probability that one of the cards is a 4 is 2/3
The answer is C.
Answer: C
Question: There are 10 points on a circle. A hexagon can be formed by linking 4 of the 10 points. How many such hexagons are possible?
Options:
A)60
B)120
C)200
D)210
E)600
Rationale: 4 points can be selected out of 10 points in 10C4 ways
=10 !/6!*4!=210
Ans D
Answer: D
Question: John draws a card from a pack of cards. What is the probability that the card drawn is a card of black suit?
Options:
A)3/78
B)4/8
C)6/5
D)1/2
E)2/3
Rationale: Explanation :
Total number of cards, n(S) = 52
Total number of black cards, n(E) = 26
P(E) =n(E)/n(S)=26/52=1/2
Answer: D
Answer: D
Question: What is the absolute value of twice the difference of the roots of the equation Q=5y^2 − 20y + 15 = 0 ?
Options:
A) 0
B) 1
C) 2
D) 3
E) 4
Rationale: Q=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: E
Question: A cyclist rides a bicycle 8 km at an average speed of 10 km/hr and again travels 10 km at an average speed of 8 km/hr. What is the average speed for the entire trip?
Options:
A)9.28
B)8.48
C)8.78
D)8.98
E)9.18
Rationale: distance = 18 km
time = 8/10 + 10/8 = (64 + 100) / 80 = 164 / 80 = 41 / 20 hours
average speed = (18 * 20) / 41 = 8.78 km/h
The answer is C.
Answer: C
Question: Question:	A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $180. The cost for 1 bat and 6 balls is $170, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $210 for the purchase?
Options:
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: IMO it should be C that is C
reason:
formed an equation... bat = b ball = c
2b+4c=180
1b+6c=170
solving both we get b that is bat = 50 and c that is ball = 20
new equation 210 to be divided in equal
3b+3c=210
3*50 + 3*20 = 210
150+60= 210
Answer: C
Question: The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Options:
A)28
B)24
C)15
D)30
E)60
Rationale: Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8
= (5 x (3/5)):(8 x (3/5))
= 3 : 24/5
A : B : C = 2 : 3 : 24/5
= 10 : 15 : 24
B = (98 x 15/49)= 30.
Answer is D.
Answer: D
Question: (8^16)+(16^10)+(4^24) = ?
Options:
A)(4)*(2^29+1)
B)(6)*(2^48)
C)(9)*(2^49)
D)(28)*(2^53)
E)2^148
Rationale: I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ)
So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents.
Here's how my brain works with this one,
Step 1: Recognize a common base.
(8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48)
Step 2: Recognize the factor and pull out of the equation.
= (2^48)(1 + (2^4) + 1)
= (2^48)(1 + 16 + 1)
= (2^48)(18)
Step 3: Recognize this is not an answer and adapt.
(2^48)(18) = (2^48)(2)(9) = 2^148
Answer is E.
Answer: E
Question: Alfred buys an old scooter for $4700 and spends $1000 on its repairs. If he sells the scooter for $5800, his gain percent is?
Options:
A)5.45%
B)6.23%
C)1.75%
D)8.12%
E)10%
Rationale: C.P. = 4700+1000 = $5700
S.P. = $5800
Gain = 5800-5700 = $100
Gain% = 100/5700 * 100 = 1.75%
Answer is C
Answer: C
Question: Fresh grapes contain 80% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 40 kgs of raisins?
Options:
A)150 kgs
B)64kgs
C)72 kgs
D)65 kgs
E)70 kgs
Rationale: The weight of non-water in 40 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-80=20% of whole weight), so
40*0.75 = x*0.2
--> x = 150.
Answer: A.
Answer: A
Question: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number E of integers that can be negative?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Minimuum should be 1
Maximum should be 4:
1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.
Negative+Negative<0
Answer:C
maximum will be 5..
you dont require both the multiplicatin to be negative for entire equation to be negative...
any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...
actually by writing minimum required as 1 out of 6,you are actually meaning 5 out of 6 also possible as you will see E=5 or 1 will give you same equation..
ans D
Answer: D
Question: 7 teams compete in a track competition. If there are 14 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 3(max wins) x 4 = 12 (4 teams win three events)
One team wins the other 2 events.
The answer is C.
Answer: C