mathewhe/aqua_rat huggingface dataset:
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 9 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 72%
(C) 120%
(D) 124.2%
(E) 138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,09 = 9/100
x= 80*9/100
x= 7.2
7.2/10 = 0.72 = 72%, Answer B
Answer: (B) 72%
Question: A grocer has a sale of Rs. 1500, Rs. 1500, Rs. 2000, Rs. 2600 for 4 consecutive months. How much sale must he have in the fifth month so that he gets an average sale of Rs. 2000?
(A) Rs. 4980
(B) Rs. 3400
(C) Rs. 4000
(D) Rs. 2400
(E) Rs. 5000
Rationale: Total sale for 4 months = Rs. (1500+1500+2000+2600) = Rs. 7600
Required sale = Rs. [ (2000 x 5) - 7600]
= Rs. (10000 - 7600)
= Rs.2400.
D
Answer: (D) Rs. 2400
Question: A man is 18 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 21 years
(B) 22 years
(C) 23 years
(D) 12 years
(E) 16 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+18.
=> 2(x+2) = (x+18+2)
=> 2x+4 = x+20
=> x = 16 years
Option E
Answer: (E) 16 years
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?
(A) 7 min to empty
(B) 5 min to full
(C) 4 min to full
(D) 2 min to empty
(E) 6 min to empty
Rationale: 1/6-1/10 == 1/15
1/15:2/5::1 : x
2/5*15 = 6 min
ANSWER E
Answer: (E) 6 min to empty
Question: The distance between two cities A and B is 870 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?
(A) 09 PM
(B) 07 PM
(C) 03 PM
(D) 05 AM
(E) 03 AM
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] = 870.
Therefore, 60x + 75(x-1) = 870.
=> x=7.
So,they meet at (8+7) i.e, 15 =>3PM
Answer: C)
Answer: (C) 03 PM
Question: If the average marks of three batches of 45, 50 and 35 students respectively is 40, 50,55, what is the average marks of all the students?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: Average marks of batch1 = 40
Students in batch1 = 45
Total marks of batch1 = 45 × 40=1800
Average marks of batch2 = 50
Students in batch2 = 50
Total marks of batch2 = 50 × 50=2500
Average marks of batch3 = 55
Students in batch3 = 35
Total marks of batch3 = 35 × 55=1925
Total students = 45+50+35 = 130
Average marks of all the students =1800+2500+1925 /130 =47.88
ANSWER:C
Answer: (C) 48
Question: What would happen in the previous question if both A and B had started at point P.
(A) 800 Km
(B) 600 Km
(C) 1000 Km
(D) 350 Km
(E) 250 Km
Rationale: DETAILED SOLUTION
For 22nd meeting, total distance travelled = 22 x 2 x 1400 Km
Distance travelled by A = 5/7∗44∗1400=44000Km (1400 x 31 + 600).Therefore, A would be 600 Km from Q.
CORRECT ANSWER B
Answer: (B) 600 Km
Question: The number 311311311311311311311 is:
(A) divisible by 3 but not by 11
(B) divisible by 11 but not by 3
(C) divisible by both 3 and 11
(D) neither divisible by 3 nor by 11.
(E) None of thses
Rationale: Sum of digits= 35 and so it is not divisible by 3.
(Sum of digits at odd places)- (Sum of digits at even places)= 19-16=3, not divisible by 11.
So, the given number is neither divided by 3 nor by 11.
Answer: D
Answer: (D) neither divisible by 3 nor by 11.
Question: What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively
(A) 56.25
(B) 60
(C) 52.5
(D) 5.25
(E) None of these
Rationale: a +10d = 5.25, a+6d = 3.25, 4d = 2, d = ½
a +5 = 5.25, a = 0.25 = ¼, s 15 = 15/2 ( 2 * ¼ + 14 * ½ )
= 15/2 (1/2 +14/2 ) = 15/2 *15/2 =225/ 4 = 56.25
ANSWER:A
Answer: (A) 56.25
Question: Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?
(A) 10%
(B) 16%
(C) 70%
(D) 80%
(E) 20%
Rationale: Let the rate of interest during the second year be R%. Given,
4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544
R = 10%
Answer:A
Answer: (A) 10%
Question: A number is increased by 20% and then decreased by 20%, the final value of the number is ?
(A) does not change
(B) decreases by 2%
(C) increases by 4%
(D) decreases by 4%
(E) None of these
Rationale: Here, x = 20 and y = - 20
Therefore, the net % change in value
= ( x + y + xy/100)%
= [20 - 20 + (20x - 20)/100]% or - 4%
Since the sign is negative, there is a decrease in value by 4%.
ANSWER:D
Answer: (D) decreases by 4%
Question: The sum of prime numbers that are greater than 60 but less than 70 is
(A) 67
(B) 128
(C) 191
(D) 197
(E) 260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum of 61 and 67 is 128.
Answer B.
Answer: (B) 128
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent K of the gasoline in the tank is brand Z?
(A) 50%
(B) 40%
(C) 37.5%
(D) 331⁄3%
(E) 25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) K= 3/8 = 37.5%
Answer (C)
Answer: (C) 37.5%
Question: A seller bought tea powder packet at 6 for each, how many for a rupee must he sell to gain 20%?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 10
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs.	6
5
For Rs.	6	, toffees sold = 6.
5
For Re. 1, toffees sold = 6 x	5 = 5
6
A
Answer: (A) 5
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
(A) 125/167
(B) 125/118
(C) 125/126
(D) 125/128
(E) 125/129
Rationale: Required probability
= 1 - 1/126 = 125/126
Answer: C
Answer: (C) 125/126
Question: The number of boys in a class is 4/5 times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
(A) A)48
(B) B)44
(C) C)42
(D) D)40
(E) E)36
Rationale: Explanation:
Let number of girls = x and number of boys = 0.8x.
Then, 0.8x + x = 1.8x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 1.8.
Answer: E
Answer: (E) E)36
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 16 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(A) 40
(B) 50
(C) 64
(D) Data inadequate
(E) None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=16
â‡’ G - S = 64
Answer C
Answer: (C) 64
Question: A house wife saved $2.50 in buying an item on sale. If she spent $25 for the item, approximately how much percent she saved in the transaction?
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) 12%
Rationale: Actual price = 25+2.50 = $27.50
Saving = 2.50/27.50 * 100 = 100/11 = 9% approximately
Answer is B
Answer: (B) 9%
Question: Find the amount on Rs.4000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 4368
(B) 6369
(C) 5460
(D) 5635
(E) 6734
Rationale: 4000 * 104/100 * 105/100
=> 4368
Answer:A
Answer: (A) 4368
Question: There are 1500 jelly beans divided between two jars, Jar X and Jar Y. If there are 200 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
(A) 1050
(B) 1075
(C) 1100
(D) 1125
(E) 1150
Rationale: X+Y=1500 so Y=1500-X
X=3Y-200
X=3(1500-X)-200
4X=4300
X=1075
The answer is B.
Answer: (B) 1075
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2000 less than the principal. What was the principal?
(A) 1500
(B) 2500
(C) 2507
(D) 3200
(E) 11500
Rationale: P - 2000 = (P*5*4)/100
P = 2500
Answer: B
Answer: (B) 2500
Question: If the average of 201, 202, 204, 205, 206, 209, 209, 210, 212 and x is 207, what is the value of x?
(A) 207
(B) 209
(C) 211
(D) 212
(E) 213
Rationale: Sum of the deviations of the numbers in the set from the mean is always zero
201, 202, 204, 205, 206, 209, 209, 210, 212
mean is 207
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 207+ 5 = 212
D
Answer: (D) 212
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 130 m long?
(A) 39.2 sec
(B) 35 sec
(C) 44 sec
(D) 40 sec
(E) none of these
Rationale: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 130 = 490 meter
Time taken to cross the platform = 490/(25/2) = 490 Ã— 2/25 = 39.2 seconds
ANSWER:A
Answer: (A) 39.2 sec
Question: The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?
(A) 10
(B) 14
(C) 38
(D) 48
(E) 47
Rationale: diagonal=10
2(l+b)+d=38
ANSWER:C
Answer: (C) 38
Question: In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 23/48
(B) 11/16
(C) 15/32
(D) 14/36
(E) 17/56
Rationale: The answer is A
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number 6 =1/6
Probability picking a spades card =1/4
so, Probability win by getting heads= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Answer: (A) 23/48
Question: If y is an integer, which of the following must be an even integer?
(A) y^2-y-1
(B) y^2-4y+6
(C) y^2-5y+5
(D) y^2+3y+8
(E) y^2+2y+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: y^2-y-1 = -1 { If y = 1 }
B: y^2-4y+6 = 3 { If y = 1 }
C: y^2-5y+5 = 1 { If y = 1 }
D: y^2+3y+8 = 12 { If y = 1 }y^2+3y+8 = 18 { If y = 2 }
E: y^2+2y+10 = 13 { If y = 1 }
Thus the only possible answer is (D)
Answer: (D) y^2+3y+8
Question: At a meeting of 5 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
(A) 9
(B) 12
(C) 15
(D) 18
(E) 21
Rationale: 5 people can be arranged around a table in 4! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 4 units around a table is 3!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 4! - 2*3! = 2*3! = 12
The answer is B.
Answer: (B) 12
Question: If 11.25 m of a uniform iron rod weight 42.75 kg, what will be the weight of 6 m of the same rod ?
(A) 22.8 kg
(B) 25.6 kg
(C) 28 kg
(D) 26.5 kg
(E) None of these
Rationale: Solution
Let the required weight be x kg. Then, Less length, Less weight
∴ 11.25 : 6 :: 42.75 : x ⇔ 11.25 × x = 6 × 42.75 ⇔ x = ⇔ x = (6x42.75)/11.25=22.8. Answer A
Answer: (A) 22.8 kg
Question: If a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a?
(A) 10
(B) B.13
(C) 18
(D) 26
(E) 50
Rationale: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Answer: (B) B.13
Question: The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
(A) 377
(B) 268
(C) 297
(D) 272
(E) 100
Rationale: 2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
Answer: E
Answer: (E) 100
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
(A) 10 kmph
(B) 11 kmph
(C) 12 kmph
(D) 13 kmph
(E) 13 kmph
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: (C) 12 kmph
Question: select which is different..342,511,126,215.
(A) 342
(B) 511
(C) 126
(D) 215
(E) can't be calculated
Rationale: 7*7*7=343,343-1=342
8*8*8=512,512-1=511
5*5*5=125,125+1=126
6*6*6=216,216-1=215
answer C
Answer: (C) 126
Question: A man invests Rs. 7,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
(A) Rs. 1200
(B) Rs. 1300
(C) Rs. 3500
(D) Rs. 2000
(E) None of these
Rationale: Explanation :
Interest on Rs.7000 at 5% per annum = ( 7000 × 5 × 1) / 100 = Rs. 350
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (7000 + x) × 6 × 1/100.
=> 350 + 2x/25 = (7000 + x) × 6 × 1/100.
=> 35000 + 8x = (7000 + x) × 6.
=> 35000 + 8x = 42000 + 6x.
=> 2x=7000.
=> x=3500.
Answer : C
Answer: (C) Rs. 3500
Question: If xy > 0, which of the following must be negative?
(A) -x/y
(B) x/y
(C) x+y
(D) x^2
(E) y^2
Rationale: Given xy> 0 So both will be the positive integers. If both are positive, then B,C,D,E also positive.
Answer : A
Answer: (A) -x/y
Question: One tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to
(A) 142 seconds
(B) 150 seconds
(C) 177 seconds
(D) 200 seconds
(E) 270 seconds
Rationale: Tap 1 : 283 secs
Tap 2 : 287 secs
Considering the average of these 2 taps : 285 secs.
So 1 tap can fill the tank in 285 secs, so 2 taps can fill the tank in 285/2 = 142.5 secs.
Closest answer is A.
Answer: (A) 142 seconds
Question: A BAG CONTAINS 6 RED AND 4 BLUE BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
(A) 4/15
(B) 5/15
(C) 6/15
(D) 7/15
(E) 8/15
Rationale: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Option: D
Answer: (D) 7/15
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
(A) 210 m
(B) 230 m
(C) 240 m
(D) 260 m
(E) 270 m
Rationale: Speed =72x(5/18) m/sec =20m/sec
Time = 26 sec.
Let the length of the train be x metres.
(x+250)/26 =20
x + 250 = 520
x = 270.
answer :E
Answer: (E) 270 m
Question: A man walks at a speed of 6 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 1 4/2 hours
(B) 1 5/8 hours
(C) 2 1/6 hours
(D) 2 1/1 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/6 + (5 1/4)/7
= 1 5/8 hours.
Answer:B
Answer: (B) 1 5/8 hours
Question: A sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution. If 60 cubic centimeters of the solution were poured into an empty container, how many grams of sucrose would be in the container?
(A)  4.00
(B)  6.00
(C)  5.50
(D)  6.50
(E)  6.75
Rationale: We are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of sucrose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of sucrose would be in the container when we have 60 cubic centimeters of solution, we can set up a proportion.
We can say: “10 grams of sucrose is to 100 cubic centimeters of solution as x grams of sucrose is to 60 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
10/100 = x/60
When we cross multiply we obtain:
(10)(60) = 100x
600 = 100x
6.00 = x
There are 6.00 grams of sucrose in the solution in the container.
The answer is B.
Answer: (B)  6.00
Question: The workforce of Company X is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
(A) 160
(B) 220
(C) 240
(D) 360
(E) 420
Rationale: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+20)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+20)
0.05x=11
x=220 - this is quantity of employees before adding 2020 men
So after adding it will be 240
Answer is C
Answer: (C) 240
Question: The product of the squares of two positive integers is 9. How many pairs of positive integers satisfy this condition?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Ans:B - 1 pairs
(xˆ2)(yˆ2) = 9 [square root both sides]
xy = 3
3 = 1x3, 3x1
Cancel the repeats
This leaves us with exactly 1 options.
Hence, B
Answer: (B) 1
Question: If xy ≠ 0 and x^2y^2 − 3xy = 28, which of the following could be y in terms of x?
I. 1/(2x)
II. -4/x
III. 7/x
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III only
Rationale: (x^2)(y^2) – 3xy - 28 = 0
(xy – 7)(xy + 4) = 0
xy – 7 = 0 or xy + 4 = 0
xy = 7 or xy = -4
Since we need y in terms of x, we can isolate y in both of our equations.
y = 7/x or y = -4/x
Answer: E
Answer: (E) II and III only
Question: 4, 7, 13, 25, 49, (...)
(A) 22
(B) 35
(C) 97
(D) 32
(E) 25
Rationale: Explanation :
4
4 × 2 - 1= 7
7 × 2 - 1 =13
13 × 2 - 1 = 25
25 × 2 - 1 = 49
49 × 2 - 1 = 97
Answer : Option C
Answer: (C) 97
Question: What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?
(A) 20 cm
(B) 23 cm
(C) 25cm
(D) 10 cm
(E) 28 cm
Rationale: Required length = HCF of 800 cm, 420 cm, 1220 cm = 20 cm
Answer is A
Answer: (A) 20 cm
Question: For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 3, -3, 2, 5, -4, -6 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Given sequence: {1, -3, 2, 5, -4, -6}
The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.
So there are 3 pairs of consecutive terms of the sequence for which the product is negative.
Answer: A.
Answer: (A) 1
Question: It is required to seat 3 boys and 2 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
(A) 28
(B) 21
(C) 30
(D) 22
(E) 12
Rationale: Total number of candidates = 3 + 2 = 5. In the row of 5 positions, the even places are 2nd, 4th.
Now, number of even places = 2.
Number of girls to occupy the even places = 2.
Even places can be filled = P (2, 2) ways.
Number of boys = 3.
The remaining 3 places can be filled by 3 boys = P (3, 3) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(2, 2) x P(3, 3) = 2! x 3! = 2 x 6 = 12
ANSWER:E
Answer: (E) 12
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 20%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
(A) 66.67
(B) 35
(C) 48
(D) 65
(E) 67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 20%, therefore bringing down the price to $60.
4) Now 60 has to be added byX %in order to equal the original price.
60 + ( X% ) 60 = 100.
Solving this eq for X, we get X = 66.67
Ans is A.
Answer: (A) 66.67
Question: walking at ¾ of his usual speed ,a man is late by 2 ½ hr. the usual time is
(A) 7 1/9
(B) 7 1/2
(C) 7 1/5
(D) 7 1/8
(E) 7 1/7
Rationale: Usual speed = S Usual time = T Distance = D New Speed is ¾ S New time is 4/3 T 4/3 T – T
= 5/2 T=15/2
= 7 1/2
Aswer: B
Answer: (B) 7 1/2
Question: United Telephone charges a base rate of $6.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
(A) 20 minutes
(B) 110 minutes
(C) 120 minutes
(D) 140 minutes
(E) 160 minutes
Rationale: Lets take number of minutesx.
Given that, 6+0.25x=12+0.2x ->0.05x=2 -> x=120minutes
ANS C
Answer: (C) 120 minutes
Question: Eight people are on an elevator that stops at exactly 8 floors. What is the probability that exactly one person will push the button for each floor?
(A) 8!/8^8
(B) 8^8/8!
(C) 8/8!
(D) 8/8^8
(E) 1/8^8
Rationale: Each person out of 8 has 8 options, hence total # of outcomes is 8^8;
Favorable outcomes will be 8!, which is # of ways to assign 8 different buttons to 8 people
So basically # of arrangements of 8 distinct objects: 8!.
P=favorable/total=8!/8^8
Answer: A.
Answer: (A) 8!/8^8
Question: How long does a train 150 m long traveling at 36 kmph takes to cross a signal post?
(A) 8 sec
(B) 15 sec
(C) 20 sec
(D) 10 sec
(E) 22 sec
Rationale: D = 150 m
S = 36 * 5/18 = 10
T = 150 * 1/10 = 15 sec
ANSWER:B
Answer: (B) 15 sec