divelab/Sys2Bench huggingface dataset:
Question: The ratio of men to women in the Snyder community choir is 4 to 7. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
Options:
A)20
B)24
C)28
D)32
E)34
Rationale: This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.
We're told that the ratio of the Men to Women in the Snyder choir is 4 to 7, so the number of men MUST be a multiple of 4 and the number of women MUST be a multiple of 4 The question asks how many WOMEN are in the SNYDER choir, so the answer MUST be a multiple of 7. We can eliminate AnswersA, B, D and E (since they're NOT multiples of 7
Answer C
Answer: C
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
Options:
A)78
B)54
C)96
D)Cannot be determined
E)56
Rationale: Answer: Option D
Let the ten's digit be x and unit's digit by y
Then, x + y = 15 and x - y = 3 or y - x = 3
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9
So, the number is either 96 or 69.
Hence, the number cannot be determined.
Answer: D
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 25 =
Options:
A)6
B)10
C)12
D)5
E)8
Rationale: D 5
Answer: D
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Options:
A)22
B)32
C)77
D)66
E)8
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
nswer: B
Answer: B
Question: In store A there are 10 pairs of pants for every 50 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
Options:
A)3:16.
B)2:3.
C)4:15.
D)3:4.
E)2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
10x : 50x
X:5X
Price :
4y:3y
Total revenue
4xy : 15xy
4:15
Answer : C
Answer: C
Question: The area of one square is x^2 + 6x + 9 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 52, what is the value of x?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: The areas are (x+3)^2 and (2x-5)^2.
The lengths of the sides are x+3 and 2x-5.
If we add the two perimeters:
4(x+3) + 4(2x-5) = 52
12x = 60
x = 5
The answer is C.
Answer: C
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: B
Question: Find the value of x in 5(x+4)=25
Options:
A)1
B)1.5
C)2
D)2.5
E)3
Rationale: 5(x+4)=25
Dividing both sides by 5 gives (x+4)=5
Subtracing both sides with 4 gives x=1
Answer: A
Answer: A
Question: When positive integer D is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when D is divided by B?
Options:
A) 13
B) 14
C) 15
D) 16
E) 17
Rationale: the remainder will be obtained from the decimal part when D is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 D=174 and B=40
Answer: B
Question: Jancy invested an amount of Rs. 9,000 at the rate of 10% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
Options:
A)15800
B)12800
C)11800
D)16800
E)17800
Rationale: Let the second amount be Rs. x. Then,
(9000 * 10 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100
9000+ 15x= 16800 + 14x
x = 7800
Total investment = 10000 + 7800 = Rs. 17,800.Answer: E
Answer: E
Question: How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
Options:
A)59
B)11!/(2!*2!*2!)
C)56
D)76
E)11!/(3!*2!*2!*2!)
Rationale: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 76.
Answer: D.
Answer: D
Question: Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following R must be true?
I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.
Options:
A)I only
B)II only
C)III only
D)I and III only
E)R=None of the above
Rationale: Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3.
Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect.
Even if not, we can rule them both out. So, E.
Answer: E
Question: Tom, working alone, can paint a room in 8 hours. Peter and John, working independently, can paint the same room in 4 hours and 2 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Options:
A)4/7
B)5/7
C)6/7
D)1/7
E)3/7
Rationale: Let the time when all three were working together be t hours. Then:
Tom worked for t+4 hour and has done 1/8*(t+4) part of the job;
Peter worked for t+2 hour and has done 1/4*(t+2) part of the job;
John worked for t hours and has done 1/2*t part of the job:
1/8*(t+4)+1/4*(t+2)+1/2*t=1 --> multiply by 8 --> (t+4)+(2t+2)+4t=8 --> t=2/7;
Hence Peter has done 1/4*(2/7+2)=1/4 *16/7=16/28 =8/14 =4/7
Answer: A
Answer: A
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
Options:
A)76 days
B)98 days
C)32 days
D)45 days
E)24 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer: C
Answer: C
Question: Calculate the largest 3 digit number which is exactly divisible by 89?
Options:
A)911
B)969
C)979
D)977
E)971
Rationale: Largest 4 digit number is 999
After doing 999 ÷ 89 we get remainder 20
Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979
C
Answer: C
Question: If a, b are integers and |a-b|=12, which of the following is the smallest possible value of ab?
Options:
A)-16
B)0
C)-36
D)7
E)40
Rationale: a=6, b=-6. Hence, the answer is C.
Answer: C
Question: Find the sum of first 80 odd numbers
Options:
A)6400
B)8000
C)5000
D)4980
E)4960
Rationale: Explanation:
n2 = 802 = 6400
Answer: Option A
Answer: A
Question: Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
Options:
A)17 kmph
B)19 kmph
C)15 kmph
D)12 kmph
E)16 kmph
Rationale: D
12 kmph
Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer: D
Question: Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King
Options:
A)1/29
B)1/26
C)1/26
D)1/25
E)1/22
Rationale: Explanation:
Let X be the event that cards are in a club which is not king and other is the king of club.
Let Y be the event that one is any club card and other is a non-club king.
Hence, required probability:
=P(A)+P(B)
=\inline {\color{Black}[(12C_{1}\times 1C_{1})/52C_{2}]+[(13C_{1}\times 3C_{1})/52C_{2}]}
Answer: B) 1/26
== =
Answer: B
Question: Find the constant k so that : -x2 - (k + 10)x - 8 = -(x - 2)(x - 4)
Options:
A)11
B)12
C)16
D)14
E)15
Rationale: -x2 - (k + 10)x - 8 = -(x - 2)(x - 4) : given
-x2 - (k + 10)x - 8 = -x2 + 6x - 8
-(k + 10) = 6 : two polynomials are equal if their corresponding coefficients are equal.
k = -16 : solve the above for k
correct answer C
Answer: C
Question: Multiply: (x – 4)(x + 5)
Options:
A)(a) x2 + 5x - 20
B)(b) x2 - 4x - 20
C)(c) x2 - x - 20
D)(d) x2 + x - 20
E)(e) x2 + x + 20
Rationale: (x – 4)(x + 5).
= x(x + 5) -4(x + 5).
= x2 + 5x – 4x – 20.
= x2 + x - 20
the answer is (D)
Answer: D
Question: A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?
Options:
A) d/800
B) 5d/1000
C) 125d
D) d/1000 + 25
E) 125/(1000d)
Rationale: Since you're choosing to approach this algebraically, I'm going to add some labeling to your work....
1,000 purchased for a total of D dollars.....
Each modem costs D/1,000 dollars....
Each modem is then sold for 25% ABOVE the cost:
(1.25)(D/1,000) = 1.25D/1,000
1.25D/1,000 = 125D/100,000
125/1,000 = 1/8 so....
125/100,000 = 1/800
So the sell price of each modem is D/800
Final Answer:
A
Answer: A
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)A)19.7
B)B)21
C)C)21.4
D)D)21.5
E)E)22.5
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total ta x incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A
Answer: A
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 4 minutes?
Options:
A)36
B)54
C)108
D)216
E)324
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 36 Carrots - 4 minutes,
1 standard Veggiematik machine - 9 Carrots - 1 minute,
Now
6 standard Veggiematik machine - ? Carrots - 4 minutes,
Hence = 9X6X4 =216 Carrots
Answer D
Answer: D
Question: In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m?
Options:
A)6 m/sec; 18 sec
B)5 m/s; 18 sec
C)4 m/s; 15 sec
D)3 m/s; 12 secs
E)2 m/s; 6 secs
Rationale: A can allow B to start the race 10 metres ahead, so the time A need to cover 100 meters equals to the time B needs to cover 90 meters --> 100/a = 90/b, where a and b are the rates of A and B, respectively.
A can allow B to start the race 2 seconds before A, so the time A need to cover 100 meters is 2 seconds less than the time B needs to cover 100 meters --> 100/a + 2 = 100/b.
Subtract one from another: 2 = 100/b - 90/b --> b = 5.
Answer: B.
Or directly: B needs 2 seconds more to cover 100 meters than to cover 90 meters --> 2 = 100/b - 90/b --> b = 5.
Answer: B
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 21 months?
Options:
A)18:11
B)18:15
C)21:11
D)18:121
E)18:112
Rationale: A invests Rs.8000 for 21 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*21 : (8000*4) + (4000*14)
168000 : 88000
A:B = 21:11.Answer:C
Answer: C
Question: In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?
Options:
A)16 2/3 %
B)25 percent
C)33 1/3 %
D)50%
E)75%
Rationale: 1986; 2/3
1988; 1/2
% decrease = change/ original*100
2/3−1/2 / 2/3∗100
1/6∗3/2∗100=14∗100 =25
Answer: "B"
Answer: B
Question: What will be the cost of house to decorate which area equal to 324 sq ft, if the price per foot of building is Rs. 10?
Options:
A)120
B)240
C)360
D)720
E)860
Rationale: Let the side of the square plot be a ft.
a2 = 324 => a = 18
Length of the fence = Perimeter of the plot = 4a = 72 ft.
Cost of building the fence = 72 * 10
= Rs.720.
Answer: D
Answer: D
Question: In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?
Options:
A)20 min
B)15 min
C)10 min
D)5 min
E)None of these
Rationale: Explanation :
The ratios of the speed of the fastest and the slowest is 2 : 1. Hence, they should meet only at one point at the circumference i.e the starting point (As the difference in the ratios in reduced form is 1).
For the two of them to meet for the first time, the faster shuld have completed one complete round over the slower one. Since, the two of them meet for the first time after 5 min, the faster one should have completed 2 rounds (i.e 2000 m) and the slower one should have completed 1 round (1000 in this time).
Thus the faster one would complete the race ( i.e 4000 m) in 10 min.
Answer : C
Answer: C
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 54, what is the total amount?
Options:
A)166
B)105
C)178
D)177
E)210
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 54
35 --- ? => 210
Answer: E
Answer: E
Question: Two pipes A and B can fill a cistern in 15 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)17 1/4 min
B)28 1/7 min
C)17 1/7 min
D)13 3/7 min
E)17 5/7 min
Rationale: 1/15 + 1/30 - 1/40 = 9/120
120/9 = 13 3/7
Answer:D
Answer: D
Question: A can do a job in 18 days and B can do it in 30 days. In how many days will they finish it together?
Options:
A)1/9
B)4/45
C)2/7
D)6/3
E)5/2
Rationale: Explanation:
1/18 + 1/30 = 8/90 = 4/45
So, both together will finish the work in 4/45 days.
Answer:B
Answer: B
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 4 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
Options:
A)5,500,000
B)2,400,000
C)55,000
D)28,000
E)280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 4 gms
In 400,000 cm^3 , X = 4 * 400,000 = 1,600,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 1,600,000 + 1,800,000 = 2,400,000
ANSWER:B
Answer: B
Question: In the fifth grade at Parkway elementary school there are 470 students. 300 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Options:
A)69.
B)135.
C)81.
D)91.
E)108.
Rationale: Total students = 470
Boys = 300, Girls = 170
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 170 - 35 = 135.
Correct option: B
Answer: B
Question: Two negative numbers are multiplied to give a product of 48. If the lesser number is 10 less than thrice the greater number, what is the greater number?
Options:
A)-6
B)-8
C)-5
D)-9
E)-10
Rationale: Test the options. The options give you the greater number.
(A) - 6
Triple of -6 is -18 and 10 less is -8.
-8 * -6 =48 (Correct)
Correct
Answer (A)
Answer: A
Question: A and B invests Rs.2500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)11:5
B)15:16
C)15:2
D)9:9
E)11:1
Rationale: (2.5*6 + 5*6): (4*12)
45:48 =>
15:16
Answer:B
Answer: B
Question: A number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e. What is the greatest two digit prime saturated integer ?
Options:
A)99
B)98
C)97
D)96
E)95
Rationale: e=96 = 3 * 32 = 3 * 2^5
Answer is D.
Answer: D
Question: A can finish a work in 18 days and B can do the same work in 15 days. B
worked for 10 days and left the job. In how many days A alone can finish the
remaining work?
Options:
A)5
B)6
C)3
D)2
E)1
Rationale: B's 10 day's work=10/15=2/3
Remaining work=(1-(2/3))=1/3
Now, 1/18 work is done by A in 1 day.
Therefore 1/3 work is done by A in 18*(1/3)=6 days.
ANSWER B
Answer: B
Question: A basket has 4 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
Options:
A)19/70
B)17/70
C)21/70
D)23/70
E)25/71
Rationale: Total fruits = 8Since there must be at least 3 apples,(4C3 * 4C1)/8C4 + 4C4/8C4 = 17/70.Answer:B
Answer: B
Question: When positive integer X is divided by positive integer Y, the remainder is 8. If X/Y = 96.12, what is the value of Y?
Options:
A)96
B)75
C)66.7
D)25
E)12
Rationale: When positive integer x is divided by positive integer y, the remainder is 8 --> x=qy+8;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=8 --> y=66.7.
Answer: C.
Answer: C
Question: John got a monthly raise of $237. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
Options:
A)327
B)723
C)732
D)231
E)237
Rationale: Let the 1st paycheck be x (integer).
John got a monthly raise of $ 237.
So after completing the 1st month he will get $ (x+237).
Similarly after completing the 2nd month she will get $ (x + 237) + $ 237.
= $ (x + 237 + 237)
= $ (x + 474)
So in this way end of every month his salary will increase by (E)$ 237.
Answer: E
Question: Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
Options:
A)52
B)67
C)71
D)73
E)79
Rationale: a+b= 6
b+c = 11
Refer England team: a+b+ (persons who only went to England) = 26
Persons who only went to England = 26 - (a+b) = 26-6 = 20
Refer French team: b+c+(persons who only went to France) = 26
Persons who only went to France = 26 - (b+c) = 15
Refer Italian team: a+b+c+f = 32
Now with above info.
Members of the club traveled to at least one of these three countries = Nothing but summation of all values (take only once)
Leftmost circle (England) : (20+a+b)
French: 15+c (all remaining already covered in previous circle)
Italy: f (all other variables taken in previous two circles)
(20+a+b)+(15+c)+f will give the answer
20+15+ a+b+c+f = 35+32 = 67
B is the answer.
Answer: B
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
Options:
A)20
B)22
C)23
D)26
E)30
Rationale: 36, 34, 30, 28, 24, ...
22 is next number.
ANSWER:B
Answer: B
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
Options:
A)641
B)640
C)188
D)177
E)166
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B
Answer: B
Question: 1, 9, 17, 33, 49, 73, ?
Options:
A)89
B)69
C)97
D)88
E)60
Rationale: C
97
The pattern is + 8, + 8, + 16, + 24,...
Answer: C
Question: To create paint with a certain shade of gray, one must combine 2.5 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Options:
A)145.0
B)140.0
C)347.1
D)694.4
E)705.6
Rationale: Since the ratio of Black to White is 2.5 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.5:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. A is more than half so can not be the answer, B fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: B
Question: Which of the following fractions is greater than 1/4 and less than 3/5?
1. 3/4 2. 2/5 3. 1/2 4. 4/5 5. 1/5 6. 9/10
Options:
A)4/7
B)1/5
C)2/3
D)1/8
E)1/4
Rationale: 1/4 = 0.25, 3/5 = 0.6, 1/5= 0.2, 2/3= 0.66, 4/7=0 .57,1/8= 0.125.
Clearly, 0.57 lies between 0.25 and 0.60
Therefore, 4/7 lies between 1/4 and 3/5.
Answer is A.
Answer: A
Question: A train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)277 m
B)700 m
C)600 m
D)187 m
E)1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (700 + x)/60 = 65/3
x =600 m.
Answer:C
Answer: C
Question: P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
Options:
A)7 days
B)8 days
C)13
D)5 days
E)2days
Rationale: Explanation :
Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days
ANSWER:C
Answer: C
Question: Find the length of the wire required to go 10 times round a square field containing 53824 m2.
Options:
A)15840
B)9280
C)2667
D)8766
E)66711
Rationale: a2 = 53824 => a = 232
4a = 928
928 * 10 = 9280
Answer: B
Answer: B
Question: In each term of a sequence, 7 is added to get the next term. If the first term is 3, what is the thirty-seventh term?
Options:
A) 222
B) 284
C) 252
D) 263
E) 255
Rationale: 1rst term + 36 terms = 3 + 7+7+7+7+7+7+7+...+7 (36 times)
3 + (7 x 36) = 3 + 252 = 255
Answer E
Answer: E
Question: In a locality there are ten houses in a row. On a particular night a thief planned to steal from three houses of locality. In how many ways can he plan such that no two houses are next to each other?
Options:
A)56
B)73
C)80
D)100
E)120
Rationale: Lets say we have removed the three said houses. Now we are left with 7 houses.
If we arrange these 7 houses we have 8 places to put the other 3 houses at.
_ H1 _ H2 _ H3 _ H4 _ H5 _ H6 _ H7 _
so 8C3 = 56
ANSWER:A
Answer: A
Question: Sandy is younger than Molly by 12 years. If the ratio of their ages is 7:9, how old is Sandy?
Options:
A)42
B)49
C)56
D)63
E)70
Rationale: Let Sandy's age be 7x and let Molly's age be 9x.
9x - 7x = 12
x = 6
Sandy is 42 years old.
The answer is A.
Answer: A