divelab/Sys2Bench huggingface dataset:
Question: At a dinner party, 6 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
Options:
A)1) 5
B)2) 10
C)3) 24
D)4) 32
E)5) 120
Rationale: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!
in this case, there are 6 guests, so number of distinct arrangements = 5! = 120
Answer : E
Answer: E
Question: How many 7's are there in the following series which are preceded by 6 which is not preceded by 8 ?
8 7 6 7 8 6 7 5 6 7 9 7 6 1 5 7 7 6 8 8 6 9 7 6 8 7
Options:
A)2
B)1
C)5
D)3
E)None
Rationale: total 2 are there
ANSWER:A
Answer: A
Question: Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems. Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly, still he got less than 60% problems right. How many more questions he would have to answer more to get passed
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 75 = 45.
He would have to answer 45 - 40 = 5
Answer: Option A
Answer: A
Question: Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent?
A. 11%
Options:
A)11 1/9%
B)5.26%
C)11 9/9%
D)11 5/9%
E)11 1/5%
Rationale: 950 --- 50
100 --- ? => 5.26%
Answer:B
Answer: B
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
Options:
A)4
B)4/7
C)4/11
D)5
E)5/7
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
Option B
Answer: B
Question: Evaluate 75% of 450 + 45% of 750
Options:
A)632
B)642
C)652
D)675
E)572
Rationale: Explanation:
= (75/100) * 450 + (45/100) * 750
= 675
Option E
Answer: E
Question: In a group of hens and cows, the total number of legs are 24 more than twice the number of heads. How many cows are there in the group?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Explanation :
Let the number of cows be x and the number of hens be y.
Then,
=> 4x + 2y = 2(x + y) + 24
=> 2x = 24
=> x = 12.
Answer : C
Answer: C
Question: Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
Options:
A)9
B)12
C)15
D)18
E)21
Rationale: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.
So out of 30 boxes, 6 are 10-pound boxes and 24 are 20-pound boxes.
If the average of 10 and 20-pound boxes is to be 16, the ratio of 10-pound boxes:20-pound boxes should be 2:3.
The number of 10 pound boxes remain the same so we still have 6 of them.
To get a ratio of 2:3, the number of 20-pound boxes must be 9.
We need to remove 15 of the 20-pound boxes.
The answer is C.
Answer: C
Question: Lines y=4√7·x−3 and y=3√7·x−1 intersect at what height above the x axis?
Options:
A)7√5
B)12
C)5√7
D)0
E)5
Rationale: Solve two equations for y
y=4√7·x−3
y=3√7·x−1
Set the two equations equal to each other and solve for x
4√7·x − 3=3√7·x−1
√7·x = 2
x = 2/√7
Plug x = 2/√7 into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=4√7·x−3
y=(4√7)·(2/√7)−3
y=4·2 - 3
y = 8 - 3
y = 5
Final answer:
E) 5
Answer: E
Question: For all even numbers n, h(n) is defined to be the sum of the even numbers between 2 and n, inclusive. What is the value of h(16)/h(10) ?
Options:
A) 1.8
B) 3
C) 2.4
D) 18
E) 60
Rationale: CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then
Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(16) = [(2+16)/2]*8 = 72
h(10) = (2+10)/2]*5 = 30
h(16)/h(10) = (72) / (30) = 2.4
Answer : C
Answer: C
Question: What is the least number of square tiles required to pave the floor of a room 13 m 44 cm long and 4m 44 cm broad?
Options:
A)7724
B)7804
C)4144
D)7844
E)None
Rationale: Solution
Length of largest tile = H.C.F. of 1344cm & 444cm = 12cm.
Area of each tile = (12 x 12)cm2
∴ Required number of tiles	= [1344x444/12x12]
= 4144.
Answer C
Answer: C
Question: Find the value of 80641 x 9999 = m?
Options:
A)807518799
B)806436469
C)807538799
D)806329359
E)817431046
Rationale: 80641 x 9999 = 80641 x (10000 - 1)
= 80641 x 10000 - 80641 x 1
= 806410000 - 80641
= 806329359
D
Answer: D
Question: 45 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)10
B)13
C)14
D)15
E)16
Rationale: According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 45 x 12 x 5 = 30 x 6 x X
X = 15
Hence, the number of days = 15.
ANSWER:D
Answer: D
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)49%
B)47%
C)44%
D)46%
E)43%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Answer: C
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options:
A)17/26
B)17/25
C)17/21
D)17/28
E)17/12
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 =17/25.
Answer:B
Answer: B
Question: Machine–X produces 50% of the total output and Machine-Y produces 75% of the total output. An average of 13 units out of a thousand goods manufactured by Machine-X and 4 unit of 500 units produced by Machine-X prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
Options:
A)0.19
B)0.16
C)0.1
D)0.05
E)0.01
Rationale: Suppose machine X produce 1000 units
total defective = 13
Machine Y then produces=1500 units
total defective=12
probability=25/2500
=0.01
Answer : E
Answer: E
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers succeding it. What is x+y?
Options:
A)113
B)213
C)163
D)213
E)131
Rationale: lets start from z, as per the question stem
z =5+7+16 =28
-->> z= 28
similarly, y =28+5+7
--> y = 40
similarly,, x =40+28+5
--> x =73
hence , x+y =73+40 = 113 --> x+y=113
ANSWER:A
Answer: A
Question: Find the odd man out. 1, 27, 216, 512, 1024, 1331
Options:
A)1024
B)512
C)27
D)1
E)2
Rationale: Explanation :
All given numbers except 1024 are perfect cubes. Answer : Option A
Answer: A
Question: 2^(10) + 2^(11) + 2^(12) + ... + 2^(24) + 2^(25) =
Options:
A)2^9(2^(10)-1)
B)2^9(2^(12)-1)
C)2^10(2^(14)-1)
D)2^10(2^(16)-1)
E)2^11(2^(17)-1)
Rationale: 2^(10) + 2^(11) + 2^(12) + ... + 2^(24) + 2^(25) =
2^(10)*(1+2+4+...+2^(15)) =
2^(10)*(2^(16) - 1)
The answer is D.
Answer: D
Question: On a track for remote controlled racing cars, racing car A completes the track in 55 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
Options:
A)275
B)325
C)385
D)425
E)None of these
Rationale: Time required in seconds will be LCM ( 35, 55 ) = 385
Hence, answer will be (C) 385
Answer: C
Question: The distance between two cities A and B is 600 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
Options:
A)09 AM
B)07 AM
C)01 PM
D)05 PM
E)03PM
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 600.
Therefore, 60x + 75(x-1) = 600.
=> x=5.
So,they meet at (8+5) i.e, 1p.m.
Answer: C)
Answer: C
Question: Three numbers are in the ratio 3:4:5. The largest number value is 40. Find difference between Smallest & largest number is?
Options:
A)20
B)24
C)16
D)28
E)30
Rationale: == 3:4:5
Total parts = 12
= The largest number value is 40
= The largest number is = 5
= Then 5 parts -----> 40 ( 5 * 8 = 40 )
= smallest number = 3 & Largest number = 5
= Difference between smallest number & largest number is = 5 - 3 = 2
= Then 2 parts -----> 16 (2 * 8 = 16)
C
Answer: C
Question: If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be:
Options:
A)67
B)68
C)65
D)69
E)NONE
Rationale: Solution: Total words starting with B = 4! = 24
Total words starting with E = 4! = 24
Total words starting with KB = 3!=6
Total words starting with KE = 3! = 6
Total words starting with KR = 3! = 6
If Starting word will be KUBER, then rank of KUBER,
= 24+24+18+1 = 67.
Answer A
Answer: A
Question: A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find the distance the car has covered.
Options:
A)114
B)115
C)116
D)117
E)118
Rationale: The driver did not plan the stop at C. Suppose it took x hours for him to get from C to B. Then the distance is S=40⋅x km. It took x−3060−1560=x−4560=x−34 h to drive from C to B. The distance from C to B is 32(x−34) km, which is 28 km shorter than 40⋅x, i.e.
32(x−34)+28=40x
32x−24+28=40x
4=8x
x=12hr⋅x=30min. Then the time of the trip from C to B was 30 min. The distance covered equals 3⋅32+12⋅40=96+20=116km.
So answer is C.
Answer: C
Question: Two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 100 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)12
B)11.9
C)16
D)20
E)18
Rationale: Sol.
Speed of the first train = [100 / 10] m/sec = 10 m/sec.
Speed of the second train = [100 / 15] m/sec = 6.7 m/sec.
Relative speed = (10 + 6.7) = m/sec = 16.7 m/sec.
∴ Required time = (100 + 100) / 16.7 secc = 11.9 sec.
Answer B
Answer: B
Question: The sum of all consecutive odd integers from −31 to 41, inclusive, is
Options:
A)110
B)135
C)150
D)165
E)185
Rationale: The sum of the odd numbers from -31 to +31 is 0.
Let's add the remaining numbers.
33+35+37+39+41 = 5(37) = 185
The answer is E.
Answer: E
Question: A retailer buys 40 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?
Options:
A)10
B)15
C)12
D)18
E)20
Rationale: let the market price of each pen be $1
then, Cost Price of 40 pens = $ 36 Selling Price of 40 pens =99% of $40=$ 39.60
profit %=((3.60*100)/36) %=10%
Answer A)10
Answer: A
Question: A chemical supply company has 60 liters of a 45% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
Options:
A)6
B)15
C)20
D)24
E)30
Rationale: 60 liters of a 45% HNO3 solution means HNO3 = 27 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
27 + x = 50% of (60 + x)
or x =6. Hence, A
Answer: A
Question: Three candidates contested an election and received 1136, 8636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got
Options:
A)55%
B)52.1%
C)57%
D)58%
E)59%
Rationale: Explanation:
Total number of votes polled = (1136 + 9536 + 11628) = 22300
So, Required percentage = 11628/22300 * 100 = 52.1%
Answer: Option B
Answer: B
Question: The diagonal of a rhombus are 25 m and 50 m. Its area is:
Options:
A)900
B)800
C)700
D)625
E)650
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 25 Ã— 50 ) Cm(power)2
= 25 Ã— 25 = 625 Cm(power)2
Answer is D.
Answer: D
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 50 overs to reach the target of 282 runs?
Options:
A)6.25
B)5.5
C)7.4
D)5
E)6
Rationale: Explanation:
Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 50
Run rate needed = 250/50=5
Answer: Option D
Answer: D
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is more than 18?
Options:
A)1/5
B)1/15
C)2/15
D)1/45
E)2/45
Rationale: The number of ways to choose two cards is 10C2=45.
There is only one way {9, 10} to get a sum more than 18.
P(sum more than 18)=1/45
The answer is D.
Answer: D
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 54% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
A)60%
B)50%
C)25%
D)19%
E)10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 54 - {both} + 40
{both} = 19%.
Answer: D.
Answer: D
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1200 in total compensation, how many total hours did he work that week?
Options:
A)60
B)40
C)44
D)48
E)52
Rationale: For 40 hrs = 40*16=640
Excess = 1200-640=560
For extra hours =.75(16)=12+16=28
Number of extra hrs =560/28=20
Total hrs =40+20=60
Answer A 60
Answer: A
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is?
Options:
A)33487
B)2778
C)2788
D)2200
E)2344
Rationale: Let the rate be R% p.a. Then,
(5000 * R * 2)/100 + (3000 * R * 4)/100 = 2200
100 R + 120 R = 2200
R = 10%
Answer:D
Answer: D
Question: A group consists of 4 men, 6 women and 2 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
Options:
A)400
B)240
C)287
D)278
E)281
Rationale: Explanation:
Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 2
= 240 ways.
Answer:B
Answer: B
Question: The three competitors on a race have to be randomly chosen from a group of five men and three women. How many different such trios contain at least one woman?
Options:
A)10
B)15
C)16
D)30
E)46
Rationale: Total ways of choosing the runners randomly = (5+3)C3 = 8C3 = 56
Unwanted cases = team of 3 MALE runners = 5C3 = 10
Desired cases = 56 - 10 = 46
Answer: Option E
Answer: E
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 30% more than the price of the other, what is the price of each of these two oranges?
Options:
A)Rs 5, Rs 7.50
B)Rs 11.1, Rs 14.9
C)Rs 10, Rs 16
D)Rs 12, Rs 14
E)None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 30% of x) = Rs. x + 1/3x = Rs. 4x/3
So, x + 4x/3 = 26
7x = 78
x = 11.1
The prices of the two oranges are Rs. 11.1 and Rs. 14.9
Answer : B
Answer: B
Question: What will come in place of the x in the following Number series? 1, 2, 12, 7, 23, 12, 34, x
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: There are two series here
1, 12, 23, 34, ... (Increase by 11)
2, 7, 12, ... (Increase by 5)
Hence, next term is 12 + 5 = 17
Correct Answer Choice is D
Answer: D
Question: In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/6 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
Options:
A)1/7
B)1/8
C)1/4
D)3/7
E)7/8
Rationale: Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
We're told that 1/6 of the garden is green, so, since all the flowers must be either green or yellow, we know that 5/6 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 5/6 * 1/2 = 3/7, or D.
Answer: D
Question: A man swims downstream 24 km and upstream 12 km taking 6 hours each time, what is the speed of the man in still water?
Options:
A)5
B)8
C)10
D)4
E)3
Rationale: 24 --- 6 DS = 4
? ---- 1
12 ---- 6 US = 2
? ---- 1 M = ?
M = (4+2)/2 = 3
Answer: E
Answer: E
Question: A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 66 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
Options:
A) 16
B) 20
C) 36
D) 44
E) 48
Rationale: lets say x ounces of P is mixed with Q.
=> 66-x ounces of Q is present in the mixture (as the total = 66 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(66-x) = 15
=> x = 30
=> 66-30 = 36 ounces of Q is present in the mixture.
Answer is C.
Answer: C
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.81. What is the median gasoline price?
Options:
A)$1
B)$1.81
C)$1.92
D)$2.13
E)$2.15
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.81, $1.96, $2.09, $2.11
The median gasoline price is $1.81. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: B
Question: The product of three consecutive numbers is 210. Then the sum of the smallest two numbers is ?
Options:
A)11
B)15
C)20
D)38
E)56
Rationale: Product of three numbers = 210
210 = 2*3*5*7 = 5*6*7.
So, the three numbers are 5, 6 and 7.
And Sum of smallest of these two = 5+6 = 11.
ANSWER : OPTION A
Answer: A
Question: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
Options:
A)23:89
B)72.9
C)38:3
D)78:3
E)79:3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.
Answer: Option B
Answer: B
Question: If x dollars is invested at 9 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 9 percent investment will exceed the annual income from the 8 percent investment by $48. If $2,000 is the total amount invested, how much is invested at 8 percent?
Options:
A)a. $280
B)b. $776.47
C)c. $892
D)d. $1108
E)e. $1200
Rationale: 2 equations with 2 unknowns
9x / 100 - 8y / 100 = 48
and
x + y = 2000
Solving these 2 equations, x = 1223.53 and y = 776.47
Answer B.
Answer: B
Question: If x/5 + 9/x = 14/5, what are the values of 3x - 7?
Options:
A)8 and 9
B)8 and 20
C)17 and 21
D)12 and 29
E)17 and 29
Rationale: I got the same thing B is the answer 8 or 20
Answer: B
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 2200, how many purple chips were selected?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 2200 = 1*5^2*8*11
The factor of 8 must come from the purple point value, so there is 1 purple chip.
The answer is A.
Answer: A
Question: increasing of length and breadth is proposional..length=6 which changes into 21 and breadth changes to 14..what was the previous value of breadth??
Options:
A)4
B)3
C)2
D)5
E)6
Rationale: Let previous breadth be "b"
previous ratio of length : breadth ==> 6 : b
let increased proportion be "x"
new ratio is ==> 6x : bx ==> 21 : 14
Length 6x = 21
x = 21/6 => x = 7/2
Breadth
bx = 14
b * 7/2 = 14
b = 28/7 => 4
Previous breadth = 4
ANSWER:A
Answer: A
Question: Arun and Varun appeared at an examination. Arun secured 9 marks more than Varun and his marks was 56% of the sum of their marks. What are the marks obtained by them
Options:
A)42, 33
B)42, 36
C)44, 33
D)44, 36
E)44, 37
Rationale: Explanation :
Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9)=56/100(2x+9)=>(x+9)=14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 42 and 33
Answer : A
Answer: A
Question: Compute the remainder when:
56666...66665:(2016 sixies)
is divided by 17.
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: A neat fact: note that
55=- 565 =-5665=-56665 ... (mod 17) :
This is easier to recognize when written in the form
5 =-56 =-566=- 5666=- 56666 .... (mod 17),
since 10n + 6=- n (mod 17) when n=- 5 (mod 17). Then, since
56666...66665:(2016 sixies)(mod 17)
clearly 56666...66665:(2016 sixies)=4(mod 17).
correct answer C
Answer: C
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
Options:
A)2 hours
B)4 hours
C)5 hours
D)1 hour
E)None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 4 hours, Tank A and B can effectively fill 1⁄12 × 4 = 1⁄3 of the tank.
Time taken to fill the remaining 1−(1/3) = 2/3 of the tank = (2/3)/(1/6) = 4 hours. Answer : Option B
Answer: B
Question: Mr. Ortiz has to successfully interview 90% of his assigned households. He was
assigned 500 households. He has interviewed 430 households so far. Has he met
his goal?
Options:
A)450
B)550
C)650
D)750
E)850
Rationale: No, he has not met his goal. He has only interviewed 530 households. He needs 90%
of 500.
Multiply: 500
x .90
Answer: 450
correct answer A
Answer: A
Question: The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 245, then the mean profit for the last 15 days would be
Options:
A)Rs. 200
B)Rs. 350
C)Rs. 275
D)Rs. 455
E)None of these
Rationale: Average would be : 350 = (245 + x)/2
On solving, x = 455.
Answer: D
Answer: D