divelab/Sys2Bench huggingface dataset:
Question: Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?
Options:
A)77
B)60
C)99
D)26
E)21
Rationale: Kim's wages : David's wages = Kim's 1 day work : David's 1 day work = 1/3 : 1/2 = 2:3
Kim's share = 2/5 * 150 = Rs. 60
Answer: B
Answer: B
Question: When n is divided by 19, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
Options:
A)3
B)7
C)10
D)13
E)nineteen
Rationale: N = 19 q + 6
N = 11 z + 6
Equating
19 Q + 6 = 11z +6
11z=19q
11z/19 = q
since q is an integer Z must be divisible by 19.
ANSWER:E
Answer: E
Question: On dividing 22 by a number, the quotient is 7 and the remainder is 1. Find the divisor.
Options:
A)1
B)2
C)3
D)6
E)7
Rationale: d = (D-R)/Q
= (22 - 1)/7
= 21/7 = 3
C
Answer: C
Question: An artist wishes to paint a circular region on a square poster that is 3.4 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?
Options:
A)1/pi
B)sqrt(2/pi)
C)1
D)2/sqrt(pi)
E)sqrt(5.78/pi)
Rationale: Area of the poster is 3.4x3.4 = 11.56
1/2 the area = 5.78
pi*r^2 = 5.78
r^2 = 5.78/pi
r = sqrt(5.78/pi) answer (E)
Answer: E
Question: Quentin's income is 60% less than Dev's income, and Sam's income is 25% less than Quentin's income. If Dev gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
Options:
A)8/9
B)11/12
C)8/13
D)11/13
E)12/13
Rationale: We can take some easy numbers and make calculations simpler.
Let R ( Dev's income) = 100
Q (Quentin's income) = 40%R = 40
S (Sam's income) = 75% Q = (3/4)*40 = 30
Now, if Dev gives 40% to Quentin --> Q = 40 + 40 = 80
60% given to Sam --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9=A
Answer: A
Question: If xy = 5 and x^2 + y^2 = 10, then x/y + y/x =
Options:
A)2
B)3 1/7
C)5 1/3
D)7
E)60
Rationale: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:
x^2 + y^2 = 10
xy = 5
we can calculate the answer 10/5 -> 2 so answer is A
Answer: A
Question: About the number of pairs which have 18 as their HCF and 136 as their LCM, the conclusion can be
Options:
A)only one such pair exists
B)only two such pairs exist
C)such pair is not exists
D)no pairs
E)None of these
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option: C
Answer: C
Question: The smallest number which when diminished by 2, is divisible by 12, 16, 18, 21 and 28 is
Options:
A)1008
B)1010
C)1022
D)1032
E)1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+2
= 1008 + 2
= 1010
Answer: B
Answer: B
Question: if QUESTION =DOMESTIC what will b code for RESPONSE ????
Options:
A)OMESUCEM
B)OMESICSM
C)OMESICEM
D)OMESISCM
E)OMESISCN
Rationale: Q U E S T I O N
D O M E S T I C
we can see in the word'RESPONSE' only R and P are the letters whose code is not given, by having a look on options we can say code for R is O and code for P is S(bcz common in all options).now we can easily code the word 'RESPONSE'as 'OMESICEM'
ANSWER:C
Answer: C
Question: Adams, Smith, Derek, Alex and Bob bought movie tickets in one row next to each other. What is the probability that Bob and Adams will each sit next to each other?
Options:
A) 5%
B) 10%
C) 15%
D) 20%
E) 25%
Rationale: Possible sitting position is 5! = 120
Bob and Adams Sitting next to each other is 5 Combination 2
=5!/2!(5-2)!
=120/2(6)
=120/12
= 10
Answer = B
Answer: B
Question: The l ength of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Options:
A)30%
B)40%
C)50percent
D)60%
E)70%
Rationale: Let original length = x and origina l breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
Question: A certain boxer has agreed to pay his opponent a fee of 2.5% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $225,000 after weighing in seven pounds over the specified limit, what was the boxer's purse?
Options:
A)$65,625
B)$105,000
C)$150,000
D)$183,750
E)$1,285,714
Rationale: .025*7 = .175
225000/.175 = $1,285,714
Answer: E
Answer: E
Question: Calculate how many days it will take for 10 boys to paint a 80 m long wall if 6 boys can paint a 70 m long wall in 8 days,
Options:
A)9.48 days
B)3.48 days
C)7.48 days
D)5.48 days
E)6.48 days
Rationale: The length of wall painted by one boy in one day = 70 / 6 * 1/8 = 1.46 m
No. of days required to paint 50 m cloth by 8 boys = 80/ 10 *1/ 1.46 = 5.48 days.
D
Answer: D
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
Options:
A)4000
B)345
C)5436
D)4530
E)4566
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 6 = Rs. 5436
Answer: Option C
Answer: C
Question: A, B and C, each working alone can complete a job in 6, 8 and 12days respectively. If all three of them work together to complete a job and earn $2500, what will be C's share of the earnings?
Options:
A)$1200
B)$1005.8
C)$555.6
D)$1009.2
E)$1490.7
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of C is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
C's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2500 = $555.6
Answer: C
Question: A boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?
Options:
A)16
B)10
C)14
D)12
E)8
Rationale: Explanation :
Let the number be x
22x + 308 = 44x
=> 44x - 22x = 308
=> 22x = 308
=> x = 308/22 = 154/11 = 14
Answer : C
Answer: C
Question: 5292 can be expressed as a product of primes as
Options:
A)2 × 2 × 3 × 3 × 7 × 7
B)2 × 3 × 3 × 3 × 7 × 7
C)2 × 2 × 2 × 3 × 3 × 7
D)2 × 3 × 3 × 3 × 3 × 7
E)2 x 2 x 3 x 3 x 3 x 7 x 7
Rationale: Explanation:
It is clear that 5292 = 2 x 2 x 3 x 3 x 3 x 7 x 7
Answer: Option E
Answer: E
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c-b=1
II. abc is an even integer
III. (a+b+c)/3 is an integer
Options:
A)I, II & III
B)II
C)I and II
D)II and III
E)I
Rationale: 1. c-b=1 --> a, b, c are consequitive positive integers and a<b<c then c=b+1 --> c-b=1. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.
Answer: A.
Answer: A
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 15% alcohol, is?
Options:
A)21
B)24
C)25
D)26
E)27
Rationale: 4.5 4.5
15% 85%
15% ----- 4.5
85% ------? => 25.5 - 4.5 = 21 ml
ANSWER:A
Answer: A
Question: A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders R when the order of the divisors is reversed.
Options:
A)8,5,3
B)R=4,2,1
C)R=3,2,1
D)R=6,4,2
E)None of above
Rationale: My approach would be
Three Divisors : 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2
Answer: D
Question: A question paper has 2parts, A & B, each containing 10 questions. If a student has to choose 8 from part A &5 from part B, in how many ways can he choose the questions?
Options:
A)1000
B)1040
C)1050
D)1100
E)1140
Rationale: There 10 questions in part A out of which 8 question can be chosen as = 10C8.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 10C5.
Hence, total number of ways,
=10C8*10C5
=[10!/(2!8!)]*[10!/(5!*5)]
= {10*9/2}*{10*9*8*7*6/(5*4*3*2*1)}
= 1140.
E
Answer: E
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 30km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
Options:
A)8.95km/hr
B)24.0km/hr
C)27.8km/hr
D)37.9km/hr
E)8.45km/hr
Rationale: average speed = (2*30*20)/30+20 km/hr
=24 km/hr
Answer (B)
Answer: B
Question: A rower can row upstream at 18 kph and downstream at 34 kph. What is the speed of the rower in still water?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: Let V be the rower's speed in still water.
Let S be the speed of the current in the stream
V-S = 18
V+S = 34
When we add the two equations, we get: 2V = 52
Then V = 26 kph.
The answer is C.
Answer: C
Question: The average of 15 numbers is 15. If the average of first five numbers is 14 and that of other 9 numbers is 16, then find the middle number.
Options:
A)12
B)11
C)10
D)9
E)8
Rationale: Given: Average of 15 numbers = 15, Average of 5 numbers = 14, Average of 9 numbers = 16
Average =	Total Numbers/No. of Numbers
15 =	Total Numbers/15
Therefore, total numbers = 15 x 15 = 225
Middle number = (Total numbers) – [(Average of 5 num x no of num) + ( Average of 9 num x no of num)]
= (225) – [(14 x 5) + (16 x 9)]
= (225) – [214]
= 11
Therefore, the middle number is 11
ANSWER IS B
Answer: B
Question: Mary's income is 60% more Than Tim's income and Tim's income is 60% less than Juan's income.What % of Juan's income is Mary's income.
Options:
A)124%
B)B.120%
C)64%
D)80%
E)64%
Rationale: Even I got 96%
J = 100
T = 100*0.4 = 40
M = 40*1.6 = 64
If Mary's income is x percent of J
M = J*x/100
x = M*100/J = 64*100/100 = 64
Ans:C
Answer: C
Question: A 470 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
Options:
A)41.1 sec
B)64.8 sec
C)31.8 sec
D)50.4 sec
E)none of the above
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 470 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 990 m
Time = Distance / Speed
= 990 x 18 / (5 x 55)
= 64.8 sec
Ans is :B
Answer: B
Question: A person spent Rs. 5,040 from his salary on food and 5,000 on house rent. After that he was left with 20% of his monthly salary. What is his monthly salary ?
Options:
A)22,550
B)32,550
C)52,550
D)62,550
E)12,550
Rationale: Total money spent on food and house rent = 5,040+5,000 = 10,040
Which is 100 - 20 = 80% of his monthly salary
∴ His salary = 10040x100/80 = 12550
Answer : E
Answer: E
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
Options:
A)57
B)67
C)77
D)87
E)97
Rationale: Money collected = (59.29 x 100) paise = 5929 paise.
Number of members = 5929 = 77.
Answer: Option C
Answer: C
Question: A and B together can complete work in 8 days. A alone starts working and leaves it after working for 6 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
Options:
A)4
B)8
C)5
D)12
E)7
Rationale: Explanation:
(A+B) one day work =1/8
now A does half of the work in 6 day so A can complete the whole work in 12 days
A’s one day work =1/12
B’s one day work=1/8 - 1/12= 1/24
B alone can complete the work in 24 days so half of the work in 12 days
Answer: Option D
Answer: D
Question: When all the students in a school are made to stand in rows of 46, 36 such rows are formed. If the students are made to stand in rows of 42, how many such rows will be formed ?
Options:
A)31
B)36
C)38
D)39
E)21
Rationale: Explanation:
Total number of students = 46 x 36
When arranged in rows of 42, number of rows formed are,
= 39.
Answer: D
Answer: D
Question: Complete the series 20, 19, 17, ...., 10, 5
Options:
A)15
B)16
C)13
D)14
E)12
Rationale: Explanation :
20 - 1 = 19
19 - 2 = 17
17 - 3 = 14
14 - 4 = 10
10 - 5 = 5
Answer : Option D
Answer: D
Question: Find the number which when increased by 11 is equal to 60 times the reciprocal of the number
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: Let the number be x.
A positive number (x) increased by 11 is equal to 60 times the reciprocal of the number (1/x)
x + 11 =	60
x
x2+11x-60=0
x2+15x-4x-60=0
x(x+15)-4(x+15)=0
(x+15)(x-4)=0
x = 4
The positive number (x) = 4
A
Answer: A
Question: If 15 students in a class average 75% on an exam and 10 students average 95% on the same exam, what is the average in percent for all 25 students?
Options:
A)81%
B)82%
C)83%
D)84%
E)85%
Rationale: (15*75 + 10*95) / 25 = 83%
The answer is C.
Answer: C
Question: If v, w, x, y, and z are five different prime numbers, which of the following is the smallest possible value of v + w + x + y + z?
Options:
A)24
B)26
C)28
D)30
E)32
Rationale: The sum of the five small smallest primes numbers is 2+3+5+7+11=28.
The answer is C.
Answer: C
Question: If Finn was 20 months old one year ago, how old was he, in months, x months ago?
Options:
A)x − 30
B)x − 12
C)32 − x
D)24 − x
E)30 − x
Rationale: Age Today = 20 months + 12 months (1year) = 32 months
X months ago- Today's Age - X = 32 - X
Ans- C
Answer: C
Question: A man has Rs. 520 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)97.5
B)60
C)75
D)90
E)105
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 520
16x = 520
x = 32.5.
Hence, total number of notes = 3x = 97.5.
Answer = A
Answer: A
Question: At what rate percent per annum will a sum of money double in 5 years.
Options:
A)20.0%
B)13.5%
C)11.5%
D)14.5%
E)21.5%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 5)]% = 20.0% per annum. Answer: A
Answer: A
Question: A train 165 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [165 * 3/55] sec = 9 sec
Answer: E
Answer: E
Question: A used-book dealer sells paperback books at 3 times the dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 130 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?
Options:
A)40
B)60
C)75
D)90
E)100
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 130 books were paperbacks, the dealer would earn a profit of $260.
Since the actual profit was $300, the dealer must have sold 40 hardbacks.
Then the number of paperbacks sold was 130-40 = 90.
The answer is D.
Answer: D
Question: A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village?
Options:
A)10km
B)50km
C)30km
D)25km
E)20km
Rationale: Average speed = 2xy/x+y = 2*25*4/25+4 = 200/29km/hr
Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km
Distance of the post office from the village = 40/2 = 20km
Answer is E
Answer: E
Question: Yesterday it took Robert 3 hours to drive from City X to City Y. Today it took Robert 2.5 hours to drive back from City Y to City X along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 50 miles per hour. What is the distance between city X and city Y?
Options:
A) 125.5
B) 120.5
C) 150
D) 240.5
E) 300
Rationale: 2d/50 = 5 ( because time = 3 + 2.5 - 0.5 hrs)
=> d = 125.5
Answer - A
Answer: A
Question: 87th number in the series 2, 10, 26,50,……….
Options:
A)29930
B)28930
C)27960
D)26780
E)25874
Rationale: 2+8*0=2
2+8*1=10
2+8*1+8*2=26
2+8*1+8*2+8*3=50...........
87th term
2+8*1+8*2+8*3+.......................................+8*86
2+8(1+2+3+4+....................+86)
2+8*(86/2)*(1+86)= 29930
ANSWER:A
Answer: A
Question: Two numbers when divided by a divisor leave remainders of 228 and 352 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
Options:
A)512
B)573
C)634
D)685
E)736
Rationale: Let x be the divisor.
N1 = xa + 228
N2 = xb + 352
N1 + N2 = x(a+b) + 580 = xc + 68
x(c-a-b) = 512 but we know that x > 352, thus (c-a-b) must equal 1.
The answer is A.
Answer: A
Question: A train 825 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 90 seconds. The speed of the train is:
Options:
A)33
B)27
C)27
D)50
E)81
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer:D
Answer: D
Question: A man can row 8 kmph in still water. When the river is running at 3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.75
B)5.7
C)5.76
D)5.74
E)6.8
Rationale: M = 8
S = 3
DS = 11
US = 5
x/11 + x/5 = 1
x = 3.4
D = 3.4 * 2 = 6.8 Answer: E
Answer: E
Question: If x and y are integers, what is the least positive number of 24x+20y?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: 24x+20y = 4(6x+5y) which will be a minimum positive number when 6x+5y = 1.
6(1) + 5(-1) = 1
Then 4(6x+5y) can have a minimum positive value of 4.
The answer is C.
Answer: C
Question: 100 people are attending a newspaper conference. 35 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
Options:
A)21
B)26
C)28
D)30
E)32
Rationale: {Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=100;
{Writers}=35;
{Editors}>38;
{Both}=x;
{Neither}=2x;
100=35+{Editors}-x+2x --> x=65-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=65-39=26.
Answer: B.
Answer: B
Question: How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 1001
1010
1100
2000
TOTAL NO. 4
B
Answer: B
Question: If the average (arithmetic mean) of a and b is 30 and the average of b and c is 60, what is the value of c − a?
Options:
A)25
B)60
C)90
D)140
E)It cannot be determined from the information given.
Rationale: -(a + b = 60)
b + c=120
c-a=60
B. 60
Answer: B
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)50
B)26
C)27
D)28
E)21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Answer: A
Question: A numberais squared and then multiplied by negative 3. The result of this operation W 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: W=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: B
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Options:
A)5/20
B)9/25
C)8/20
D)9/20
E)6/20
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}
answer 9/20
Answer D
Answer: D
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Options:
A)180
B)288
C)667
D)299
E)12
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A
Answer: A
Question: During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1/2 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
Options:
A)x/8
B)x/2
C)2x/5
D)3x/4
E)4x/5
Rationale: Let y be the number of total burgers.
veggie = y/6 , non veggie = 5y/6
1/4 of the rest of the burgers sold were double-meat
=> 5y/6 * 1/2 = double meat = x
=> y/6 = 2x/5 = veggie
Hence C
Answer: C
Question: In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male?
Options:
A)3/7
B)11/35
C)16/35
D)31/70
E)37/70
Rationale: Let x be the number of birds in the tree.
The fraction of birds that are male parrots is (1/3)(3/7)=1/7.
The fraction of birds that are male toucans is (3/10)(4/7)=6/35.
The total fraction of male birds is 1/7 + 6/35 = 11/35.
The answer is B.
Answer: B
Question: If f(x) = ax^3 + x^2 + ax – 2x, then f(b) – f(-b) will equal:
Options:
A)2ab^3 - 2ab
B)2ab
C)2ab^3 + 2ab - 4b
D)- 4b
E)2ab^3
Rationale: f(x)=ax^3 + x^2 + ax – 2x
f(b) = ab^3 + b^2 + ab – 2b
f(-b) = - ab^3 + b^2 - ab + 2b
f(b) - f(-b) = ab^3 + b^2 + ab – 2b + ab^3 - b^2 + ab – 2b
=2ab^3 + 2ab - 4b
Answer C
Answer: C
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 432 sq m, then what is the breadth of the rectangular plot?
Options:
A)12
B)17
C)18
D)19
E)14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 432
3b2 = 432
b2 = 144
b = 12 m.
Answer: Option A
Answer: A
Question: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)13
B)59
C)35
D)37
E)12
Rationale: Explanatory Answer
Decoding "A number when divided by a divisor leaves a remainder of 24"
Let the original number be 'a'.
Let the divisor be 'd'.
Let the quotient of dividing 'a' by 'd' be 'x'.
Therefore, we can write the division as a/d = x and the remainder is 24.
i.e., a = dx + 24
Decoding "When twice the original number is divided by the same divisor, the remainder is 11"
Twice the original number is divided by d means 2a is divided by d.
We know that a = dx + 24.
Therefore, 2a = 2(dx + 48) or 2a = 2dx + 48
When (2dx + 48) is divided by 'd' the remainder is 11.
2dx is divisible by 'd' and will therefore, not leave a remainder.
The remainder of 11 would be the remainder of dividing 48 by d.
The question is "What number will leave a remainder of 11 when it divides 48?"
When 37 divides 48, the remainder is 11.
Hence, the divisor is 37.
Choice D
Answer: D
Question: If g and s are positive integers such that (2^g)(4^s) = 16, then 2g + s =
Options:
A) 2
B) 3
C) 4
D) 5
E) 6
Rationale: lets get the eq into simplest orm..
(2^g)(4^s) = 16..
(2^g)(2^2s) = 2^4..
or g+2s=4..
since g and s are positive integers, only g as 2 and s as 1 satisfy the Equation..
so 2g+s=2*2+1=5..
D
Answer: D
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43 x
Options:
A)46
B)26
C)36
D)35
E)45
Rationale: (A)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 43 + 3 = 46.
Answer: A