divelab/Sys2Bench huggingface dataset:
Question: 1/(3-2√2)=?
Options:
A)9+4√5
B)9-4√5
C)3+2√2
D)9-2√5
E)4+9√5
Rationale: This question requires us to rationalize (fix) the denominator.
For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044
Given: 1/(3-2√2)
Multiply top and bottom by the CONJUGATE of 3-2√2, which is 3+2√2
So, 1/(3-2√2) = (1)(3+2√2)/(3-2√2)(3+2√2)
= (3+2√2)/(1)
= 3+2√2
=
C
Answer: C
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 110 mph. On the way home, I flew 72 mph. What was my average speed for the trip?
Options:
A)198 mph
B)91 mph
C)88 mph
D)100 mph
E)99 mph
Rationale: (110 mph +72 mph)/2= 91 mph
Correct answer is: B
Answer: B
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 20. He sellis the radio for Rs 300. The profit percent of the retailer is
Options:
A)22.4%
B)50%
C)25%
D)52%
E)None of these
Rationale: Explanation:
cost price = (225 + 20) = 245 sell price = 300
gain = (55/245)*100 = 22.4%. Answer: A
Answer: A
Question: John invested Rs. 3500 in a scheme for 3 years at compound interest rate 4% p.a. How much amount will John get on maturity of the fixed deposit?
Options:
A)s.4000
B)s.3578
C)s.3258
D)s.3990
E)s.3937.02
Rationale: Amount = [3500 * (1 + 4/100)3]
= 3500 * 26/25 * 26/25 * 26/25
= Rs.3937.02
Answer:E
Answer: E
Question: Martins made a part payment of $650 toward buying a brand new washing machine, which represents 15% of the total cost of the washing machine, how much remains to be paid?
Options:
A)$1116.3
B)$3583.3
C)$3283.3
D)$3683.3
E)$2683.3
Rationale: Explanation:
Let's start with what the total price of the washing machine would be. If 15% is equal to $650 then 100% equals $x. We just have to multiply $650 by 6.67 to get total amount=$4333.3. Out of this amount we then need to deduct the amount already paid which was $650 so we have $4333.3-$650=$3683.3
Answer: Option D
Answer: D
Question: In a particular 100 meter race, 7 athletes are participating that are numbered 1-7. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
Options:
A)1240
B)1860
C)2520
D)3220
E)4180
Rationale: The total number of ways for the athletes to finish is 7! = 5040.
#4 will be ahead of #2 in exactly half of these possibilities.
5040/2 = 2520
The answer is C.
Answer: C
Question: A zinc-copper alloy with 6 kg of pure zinc would contain 90% of zinc. The alloy with 4 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
Options:
A)2.4 kg or 80%
B)4.8 kg or 80%
C)3.4 kg or 60%
D)7.4 kg or 18%
E)1.4 kg or 60%
Rationale: Right Answer Explanation:
x : 6
y : 100
90
10 : 90 – y
(90-y)/6 = 10/x = ………..(1)
In the second case,
x 4
y 90
84
6 84-y
Therefore (84-y)/4 = 6/x ………..(2)
Dividing (1) and (2)
=
540 – 6y = 1260 – 15y
9y = 720
y = 80
x = 60/(90-80) = 60/10 = 6 kg
Quantity of zinc in x = 80% of x
= 0.8 6
= 4.8 kg
Weight and percentage of zinc is 4.8 kg or 80%
B
Answer: B
Question: The average (arithmetic mean) of 14, 32, and 53 is 3 more than the average of 21, 47, and x. What is x?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: The average of 14, 32, and 53 is 33.
The average of 21, 47 and x is 30.
Then 21 + 47 + x = 90.
x = 22.
The answer is C.
Answer: C
Question: A teacher gave the same test to three history classes: D, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Options:
A)74
B)75
C)76
D)77
E)78
Rationale: Ans : B (75)
lets say class D indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class D is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = D+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Answer: B
Question: The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ?
Options:
A)71
B)44
C)36
D)16
E)18
Rationale: Explanation:
Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years.
Answer: C
Answer: C
Question: Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.
Options:
A)12 , 18
B)8 , 10
C)18 , 20
D)20 , 25
E)None of these
Rationale: Explanation :
Let speed of ram and shakil be x and y resp.
Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute.
2000/x - 1800/y= -60
2000/x= 1800/y -60---------------------(1)
Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters
distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters
1000/x = (2000- 360y)/y------------------(2)
Solve equation 1 and 2 to obtain x and y
Answer is x = 8 minutes, y = 10 minutes
Hence (B) is the corret answer.
Answer : B
Answer: B
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 36∘, the temperature of Friday was :
Options:
A)44∘
B)40∘
C)38∘
D)30∘
E)None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 36. So T+W+Th=(152-36)=116
T+W+Th+F=(4×40)=160
F = (160-116)=44∘
Correct Option: A
Answer: A
Question: If 25% of x is 15 less than 15% of 1600, then x is?
Options:
A)872
B)738
C)900
D)840
E)83
Rationale: 25% of x = x/4 ; 15% of 1600
= 15/100 * 1600 = 240
Given that, x/4 = 240 - 15
=> x/4 = 225 => x = 900.
Answer:C
Answer: C
Question: Three models (K, L, and M) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model K, 17 cars of Model L, and 15 cars of Model M. What is the maximum number of cars of model K in any showroom ?
Options:
A)17
B)16
C)15
D)14
E)13
Rationale: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17).
Moreover that the number of model K is maximum means that the numbers of model L and M should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.
So Maximum number of model K is 17-2= 15.
The answer is (C)
Answer: C
Question: If x and y are integers, and x/y is not an integer then which of the following must be true?
Options:
A)x is odd and y is even
B)x is odd and y is odd.
C)x is even and y is odd
D)x<y
E)None of the above
Rationale: x and y could be co-primes
Answer could be E
Answer: E
Question: Complete the sequence:
B D H N ?
Options:
A)M
B)V
C)S
D)D
E)Z
Rationale: B+2=D
D+4=H
H+6=N
B+8=V
B
Answer: B
Question: The circulation for magazine P in 1961 was 4 times the average (arithmetic mean) yearly circulation for magazine P for the years 1962-1970. What is the ratio of the circulation in 1961 to the total circulation during 1961-1970 for magazine P ?
Options:
A)2/7
B)5/7
C)3/7
D)4/7
E)1/7
Rationale: There are 9 years from 1962-1970, inclusive. Let's say the average circulation every year between 1962-1970 inclusive is x.
So the total circulation is 9x from 1962-1970, inclusive.
In 1961, the circulation is 4x.
So total circulation for 1961-1970 is 4x + 9x = 13x.
Ratio of circulation in 1961 to total circulation during 1961-1970 is 4x to 14x or 4/14=2/7
Answer : A
Answer: A
Question: Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.
Options:
A)150 sq.cm
B)120 sq.cm
C)130 sq.cm
D)125 sq.cm
E)110 sq.cm
Rationale: Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 24 ⇒ AO = 12
Let BO = x and AB = 13 cm (given)
By Pythagorean theorem
c 2 = a 2 + b 2
13 2 = 12 2 + x 2 169 = 144 + x 2
x 2 = 169 – 144
x 2 = 25
x = 5 cm
BO = 5 cm
Diagonal BD = 2 x 5 = 10 cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 10
Area = 120 sq.cm
Answer is 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)2/5
B)9
C)9/5
D)1/5
E)9/20
Rationale: 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}.
P(E) = n(E)/n(S) = 9 /20
Answer: E
Question: In a certain town, there are two times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
Options:
A)1 to 4
B)2 to 3
C)1 to 2
D)3 to 4
E)4 to 5
Rationale: Town state: 2 times the whole town or country
then ratio will be 2(times)/3 total(times)
So the answer is 2/3.
B
Answer: B
Question: There are 4 people and 4 chairs. In how many different ways people can occupy the chairs?
Options:
A)12
B)15
C)24
D)36
E)120
Rationale: number of ways =4! = 24
Answer is C
Answer: C
Question: In the xy-coordinate system, line k passes through points (-7m, 0) and (0, 3m). Which of the following is a possible equation of line k?
Options:
A)y = -7/3*x + 3m
B)y = 3/7*x - 7m
C)y = 7/3*x + 3m
D)y = 3/7*x + 3m
E)y = -3/7*x - 7m
Rationale: The slope of the line is 3m/7m=3/7.
The y-intercept is 3m.
the equation of the line is: y = 3/7*x +3m
The answer is D.
Answer: D
Question: Ayesha's father was 34 years of age when she was born while her mother was 30 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)6
B)8
C)5
D)1
E)2
Rationale: Mother's age when Ayesha's brother was born = 30 years.
Father's age when Ayesha's brother was born = (34 + 4) years = 38 years.
Required difference = (38 - 30) years = 8 years.
Answer:B
Answer: B
Question: A coin is flipped twice.What is the probability that both flips result in heads given that first flip does?
Options:
A)1/2
B)2
C)1
D)3/2
E)1/3
Rationale: A=First flip lands heads.
B=Second flips is head.
P(b|a)=n(a intersection b)/n(a)
=P(h,h)/P[(h,h),(h,t)]
=1/2
Answer is option A
Answer: A
Question: A shopkeeper sold an book offering a discount of 5% and earned a profit of 33%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)140
B)120
C)130
D)110
E)150
Rationale: Let C.P. be $100.
Then, S.P. = $133
Let marked price be $x. Then, 95/100 x = 133
x = 13300/95 = $140
Now, S.P. = $140, C.P. = $100
Profit % = 40%.
A
Answer: A
Question: A number exceeds by 15 from its 3/8 part. Then the number is?
Options:
A)A)32
B)B)24
C)C)39
D)D)40
E)E)45
Rationale: x – 3/8 x = 15
x = 24
ANSWER:B
Answer: B
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 14 sec. What is the length of the platform?
Options:
A)287 m
B)350 m
C)267 m
D)535.71 m
E)656 m
Rationale: Speed = 300/14= 150/7 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 150/7
=> x = 535.71 m.
Answer:D
Answer: D
Question: Circles X and Y are concentric. If the radius of circle X is six 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)35/36
E)8/9
Rationale: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 6a, so area = 9. PI a ^ 2
Area of shaded region = 36PI a^2 - PI a^2 = 35 PI a^2
So, probability = ( 35 PI a^2 ) / (36 PI a^2 )
= 35/36 = Answer = D
Answer: D
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 35 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
Options:
A)80
B)90
C)95
D)121.5
E)108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 35% = 90*1.35 = 121.5
Thus ratio = 121.5/100 = 1.215 (in % terms = 121.5%). Thus D is the correct answer.
Answer: D
Question: How many Kg of rice at Rs.6.60 per Kg. be mixed with 56Kg of rice at Rs.9.60 per Kg to get a mixture
worth Rs.8.20 per Kg
Options:
A)56 Kg
B)52 Kg
C)44 Kg
D)49 Kg
E)None of these
Rationale: Explanation :
By the rule of alligation, we have
Cost of 1 kg of 1st kind rice Cost of 1 kg of 2nd kind rice
6.6 9.6
Price of 1Kg of the mixture
8.2
9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6
Quantity of 1st kind rice : Quantity of 2nd kind rice = 1.4 : 1.6 = 7 : 8
Quantity of 1st kind rice : 56 = 7 : 8
=>Quantity of 1st kind rice = 56×78=49
Answer : Option D
Answer: D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
Options:
A)17/22
B)17/29
C)17/98
D)17/20
E)17/27
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP)
= 10/20 + 8/20 - 1/20
= 17/20
Answer:D
Answer: D
Question: A one-foot stick is marked in 1/2 and 1/4 portion. How many total markings will there be, including the end points?
Options:
A)8
B)4
C)5
D)6
E)7
Rationale: LCM of 8 = 4
1/2 marking are (Table of 2) 0...... 2 ........... 4
(Total = 3)
1/4 marking are (Table of 1) 0 ....... 1 ...... 2...... 3........ 4 (Total = 5)
Overlapping markings are 0 ........ 2 ......... 4 (Total = 3)
Total markings = 3+5-3 = 5
Answer = C
Answer: C
Question: Find a two digit number, given that the sum of the digits is 13 and the difference of the digits is 5.?
Options:
A)74
B)82
C)95
D)76
E)94
Rationale: Using elimination method find which of the options fit the description of the number
... from the option only 94 meets this description
sum of digits---9+4 = 13
difference of digits ---9-4 = 5
Answer E.
Answer: E
Question: john bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that john paid, including sales tax?
Options:
A)3%
B)4%
C)7%
D)D.10%
E)12%
Rationale: For john
Cost of Computer = $2000
Sales tax = (5/100)*2000 = $100
Total Cost of Computer = 2000 + 100 = 2100
For Henry
Cost of Computer = $1800
Sales tax = (12/100)*1800 = $216
Total Cost of Computer = 1800 + 216 = 2016
% that Henry paid less than john = (2100 - 2016)*100/2100 =4%
Answer: Option B
Answer: B
Question: In how many ways can 5 boys and 2girls be arranged ata table if 2 girls are never together?
Options:
A)234
B)256
C)345
D)367
E)480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: E
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in h hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of h?
Options:
A)3/4
B)1[1/5]
C)1[2/5]
D)1[3/4]
E)2
Rationale: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * h = 1 => X = 1/h
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/h = 4/3
=> 1/h = (8-3)/6 = 5/6
=> h = 6/5 = 1[1/5]
Answer B
Answer: B
Question: The L.C.M. of 2 numbers is 54. The numbers are in the ratio 2:3. Find their sum?
Options:
A)36
B)40
C)45
D)32
E)56
Rationale: Let the numbers be 2x and 3x
L.C.M. = 6x
6x = 54
x = 9
The numbers are = 18 and 27
Required sum = 18+27 = 45
Answer is C
Answer: C
Question: Set A contains all the even numbers between 22 and 70 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Options:
A)600
B)800
C)1000
D)1200
E)1400
Rationale: Each term in set B is 40 more than the corresponding term in set A.
The difference of the sums = 25 * 40 = 1000.
The answer is C.
Answer: C
Question: Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 74% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 58% problems right. How many more questions he would have to answer more to get
passed
Options:
A)3
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 58% = 58% of total quations
= 58 % of 74 = 43.
He would have to answer 43 - 40 = 3
Answer: Option A
Answer: A
Question: If Jake loses 5 pounds, he will weigh thrice as much as his sister. Together they now weigh 285 pounds. What is Jake's present weight, in pounds?
Options:
A) 131
B) 135
C) 139
D) 147
E)215
Rationale: This problem can be solved as a simple word problem in which we must convert words to math. Before we create our equations, we want to define some variables.
J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 5 = 3S
J = 3S + 5 (Equation 1)
Next, we are told that “Together they now weigh 275 pounds.” We can also put this into an equation.
J + S = 285 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
3S + 5 = 285-S
4S = 280
S = 70
J + 70 = 285
J = 215
Answer: E
Answer: E
Question: A and B started a business with their capitals Rs. 24,000 and 36,000 respectively. Annual profit will be distributed between them in the ratio
Options:
A)1:3
B)2:3
C)4:3
D)2:1
E)2:5
Rationale: 24,000:36,000
Ans. 2:3
ANSWER:B
Answer: B
Question: Which of the following numbers is between 1⁄2 and 1⁄3?
Options:
A).55
B).38
C).29
D).22
E).20
Rationale: 1/3 = .333...
1/2 = .5
The only number between these two is 0.38.
The answer is B.
Answer: B
Question: How much time does a train 125 metres long running at 60 km/hr take to pass a pole?
Options:
A)6s
B)2.08s
C)7.5s
D)8s
E)9s
Rationale: Explanation:
60 km/hr = 60 * 5/18 = 16.67 m/s
Speed = distance/time; v = d/t
16.67 = 125/t
t = 7.5s
ANSWER C
Answer: C
Question: What is the smallest number which, when increased by 7, is divisible by 7, 8, and 24?
Options:
A)154
B)161
C)168
D)175
E)182
Rationale: LCM(7,8,24)=24x7=168
So the least divisible number is 168, and the number we are looking for is 168-7=161.
The answer is B.
Answer: B
Question: In how many ways can a group of 2 men and 2 women be made out of a total of 7 men and 5 women?
Options:
A)240
B)270
C)230
D)210
E)280
Rationale: We need to select 2 men from 7 men and 2 women from 5 women. Number of ways to do this= 7C2 × 5C2210 D)
Answer: D
Question: Two cars start from the opposite places of a main road, 140 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
Options:
A)65
B)38
C)20
D)55
E)21
Rationale: Answer: D) 55 km
Answer: D
Question: Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.
Options:
A)Rs. 610
B)Rs. 612
C)Rs. 614
D)Rs. 616
E)None of these
Rationale: Explanation:
Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112
So compound interest = (8112 - 7500) = 612
Answer: B
Answer: B
Question: A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?
Options:
A)1/31
B)1/35
C)1/37
D)2/35
E)3/37
Rationale: Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35
B)
Answer: B
Question: An increase of Rs 3 in the selling price of an article turn a loss of 15/2% into a gain of 15/2%.The cost price of the article is??
Options:
A)10 rs
B)20 rs
C)25 rs
D)30 rs
E)40 rs
Rationale: let cost price= x rs
and selling price = y rs
now condition (1)-
if we sell at y loss occurs 15/2%
so by formula
selling price ={(100-%loss)/100}* cost price
so put values
y={(100-15/2)/100}x
y=(185/200)*x
x*182/200 - y=0---------(1)
condition 2-
if we increase selling price by 3 we get profit by 15/2%
so by formula
selling price={(100+%profit)/100}*cost price
put values
y+3={(100+15/2)/100}*x
x*(215/200)-y=3 --------(2)
now on solving equation 1 and 2 we get
x= 20 rs
ANSWER:B
Answer: B
Question: A and B complete a work in 6 days. A alone can do it in 8 days. If both together can do the work in how many days?
Options:
A)3.75 days
B)3.43 days
C)2.99 days
D)2.98 days
E)2.44 days
Rationale: 1/6 + 1/8 = 7/24
24/7 = 3.43 days
Answer: B
Answer: B
Question: The addition 742586 + 829430 = 1212016 is incorrect. It can be corrected by changing
one digit d, wherever it occurs, to another digit e. Find sum of d and e.
Options:
A)1316016
B)1416016
C)1516016
D)1616016
E)1716016
Rationale: let's choose 8=2+6. So,
Consider d=2 and e=6
Therefore, changing every occurrence of 2 with 6 in the whole statement(i.e both R.H.S and L.H.S), we get
746586+869430=1616016
ANSWER:D
Answer: D
Question: If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =
Options:
A)−48
B)−5
C)2
D)-7
E)48
Rationale: i.e. if a = 2 then b = -9
or if a = -9 then b = 2
But in each case a+b = -9+2 = -7
Answer: option D
Answer: D
Question: How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest?
Options:
A)8 years
B)20 years
C)72 years
D)56 years
E)None
Rationale: In this case, Rs. 1000 has become Rs.5000.
Therefore, the interest earned = 5000 – 1000 =4000
Interest for Rs 1000 @ 20% for 1 year = 200
200 - 1
4000 - ? => 20 years
Answer : B
Answer: B
Question: 45 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
Options:
A)24
B)77
C)30
D)25
E)13
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
27 : 45 :: 18 : x
[Please pay attention, we have written 27 : 45 rather than 45 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
{\color{Blue} x=\frac{45\times 18}{27}}
x = 30
So 30 days will be required to get work done by 27 men.
Answer: C
Answer: C
Question: The greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively, is:
Options:
A)123
B)127
C)235
D)4
E)505
Rationale: Explanation:
Required number = H.C.F. of (1642 - 6) and (1856 - 4)
= H.C.F. of 1636 and 1852 = 4. Answer: D
Answer: D
Question: Indu gave Bindu Rs.7500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)5
B)2
C)9
D)5
E)12
Rationale: 7500
= D(100/4)2
D = 12
Answer: E
Answer: E
Question: A store sells brand X pens for 5 dollars each, brand Y pens for $4 each and brand Z pens for $3 each. There are a total of 36 of these three types of pens in the store, the number of brand X pens is twice sum of the number of brand Y pens and brand Z pens, and the difference of the number of brand Y pens and the number of brand Z pens is 2. What is the largest possible total amount that three types of pens will be sold for?
Options:
A)$163
B)$159
C)$156
D)$148
E)$125
Rationale: Max price = 5X+4Y+3Z -------(1)
Given: X+Y+Z = 36 -------(2)
Given: X = 2(Y+Z) --------(3)
Substitute (3) in (2) Y+Z = 12 -----(4)
Given: Y-Z = 2 ----(5)
Using equations (4) and (5) Y = 7 and Z = 5.
Substitute Y and Z in 3 we get X = 24
Substitute X, Y and Z in (1) we get answer = 163 i.e.
ANSWER:A
Answer: A