mathewhe/aqua_rat huggingface dataset:
Question: A warehouse is labeling computer inventory with 3-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 3-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 3-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
(A) 981
(B) 1000
(C) 1011
(D) 1101
(E) 100
Rationale: The number of codes possible if leading zero is allowed = 10*10*10=10^3
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3
The difference = 10^3 - 9*10^2 = 10^2(10-9) = 10^2.
Answer: E
Similar questions to practice:
Hope it helps.
Answer: (E) 100
Question: A man has Rs. 512 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 33
(B) 38
(C) 37
(D) 90
(E) 96
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 512
⇒ 16x = 512
∴ x = 32.
Hence, total number of notes = 3x = 96
Answer:E
Answer: (E) 96
Question: A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 85 on the S scale?
(A) 39
(B) 41
(C) 43
(D) 45
(E) 47
Rationale: A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(85)/5 - 12 = 51-12 = 39
The answer is A.
Answer: (A) 39
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $60, what was the final price of the sweater?
(A) $31.5
(B) $35.75
(C) $15.75
(D) $ 45.75
(E) $17.75
Rationale: The price with 30% off
60 - 30% of 60 = 60 - (30 / 100) *60 = 42
The price with another 25% off
42 - 25% of 42 = 42 - (25/100)* 42 = $31.5
correct answer A
Answer: (A) $31.5
Question: The product of two successive numbers is 1122. Which is the smaller of the two numbers?
(A) 34
(B) 36
(C) 33
(D) 38
(E) 31
Rationale: C
33
From the given alternatives,
33 × 34 = 1122
∴ Smaller number = 33
Answer: (C) 33
Question: How many integers between 1 and 1,800 are divisible by 20,30,40?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: LCM of the given numbers=120
Therefore , number of integers = 1800/120
=15
Option B is answer
Answer: (B) 15
Question: How many different arrangements of letters are possible if three letters are chosen from the letters A through F and the letters E and A must be among the letters selected?
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40
Rationale: Besides A and E, there are 4 letters and we can choose one of them.
4C1 = 4
Three letters can be arranged in 3! ways.
The number of arrangements is 4*3! = 24
The answer is A.
Answer: (A) 24
Question: At the end of a business conference the 8 people present all shake hands with each other once. How many handshakes will there be altogether ?
(A) 20
(B) 28
(C) 55
(D) 90
(E) 95
Rationale: number of handshakes = 8C2= 8*7/2 = 28
ANSWER:B
Answer: (B) 28
Question: A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is :
(A) 2.5 km/hr
(B) 4.2 km/hr
(C) 5 km/hr
(D) 10.5 km/hr
(E) None of these
Rationale: Solution
Speed of stream =1/2(13-8) kmph = 2.5 kmph. Answer A
Answer: (A) 2.5 km/hr
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
(A) 756
(B) 700
(C) 600
(D) 500
(E) 450
Rationale: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756.
ANSWER A
Answer: (A) 756
Question: If f(x)=1/x and x is a natural number, what CANNOT be the answer for f(f(x))?
(A) 1/7
(B) 3
(C) 12/3
(D) 6/6
(E) 1
Rationale: Answer A is impossible because the invers of 1/x is x, and the only way to have something other than a natural number is to input something other than a natural number. With the specification that only natural numbers may be used 1/7 is not a possibility for f(f(x))
Answer: (A) 1/7
Question: A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage
(A) 10% Loss
(B) 10% gain
(C) 20% Loss
(D) 30% Loss
(E) 40% Loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
A
Answer: (A) 10% Loss
Question: There are 9 magazines lying on a table; 4 are fashion magazines and the other 5 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
(A) 1/2
(B) 2/3
(C) 32/35
(D) 20/21
(E) 13/14
Rationale: answer is D
Total probability=9C3=84
5C3 +5C2*4C1+5C1*4C2=10+40+30=80
therefore the probability that at least one of the fashion magazines will be selected= 80/84=20/21
D
Answer: (D) 20/21
Question: The sum of money will be double itself in 30years and simple interest find rate of interest?
(A) A)2.33%
(B) B)3.33%
(C) C)4.33%
(D) D)5.33%
(E) E)6.33%
Rationale: T = 30 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/30x =3.33%
Answer is B
Answer: (B) B)3.33%
Question: The difference between a two-digit number and number obtained by interchanging the two digits is 63. What is the difference between the two digits of that number?
(A) 29
(B) 70
(C) 92
(D) 8
(E) 7
Rationale: Let the ten’s digit be x and unit’s digit be y
(10x+y)-(10y+x)=63
9(x-y)=63
x-y=7
Option E
Answer: (E) 7
Question: The total of company C's assets in 1994 was 700% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
(A) 7N
(B) 18N
(C) 29N
(D) 32N
(E) 40N
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 = $500
In 1994, the total assets were 700% GREATER than they were in 1993, which means 1993 PLUS 700% of 1993:
$500 + 7x$500 = $500 + $3500 = $4000
This is 40 times the 1992 number, so the correct answer is 40N.
Answer: (E) 40N
Question: Ten years ago, the ratio of ages of P and Q was 3:2. Ten years from now, the ratio of their ages will be 7:6. What is P's age at present?
(A) 18
(B) 20
(C) 21
(D) 24
(E) 25
Rationale: 2(P-10)/3 = (Q-10). Then Q = 2(P-10)/3 + 10
6(P+10)/7 = Q+10
6(P+10)/7 = 2(P-10)/3 + 20
18P+180 = 14P + 280
4P = 100
P = 25
The answer is E.
Answer: (E) 25
Question: A security company can use number 1 -7 to create a 5 digit lock combo. No numbers can be repeated and the first and last digit must be odd. How many unique lock combos can be created?
(A) 60
(B) 120
(C) 180
(D) 240
(E) 300
Rationale: Lets take it this way, first and last digit needs to be odd so that means it take 1,3,5,7
So, for first digit we have 4 options and for last digit we have 3 digits
for the rest of the 3 digits we have 5 digits to choose from so 5C3=105C3=10 options
Total combinations = 4 * 3 * 10 = 120
ANS:B
Answer: (B) 120
Question: A student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: xC1 * (x-1)C1=56
x^2 -x -56 =0
(X-8) (X+7) = 0
X= 8 , -7
-7 can't possible.
Hence 8 should be the answer
B
Answer: (B) 8
Question: Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is :
(A) Rs.1500
(B) Rs.1600
(C) Rs.1625
(D) Rs.1650
(E) None
Rationale: Explanation:
Ratio of rents
=(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3)
=72:50:140:63
Let total rent = Rs.x
Then, A's share = Rs.(x×72/325)= Rs.(72x/325)
72x/325=360 or x = 325×360/72=1625
Correct Option: C
Answer: (C) Rs.1625
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock K was $15. If the price per share of stock K was $16 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
(A) 1.4%
(B) 5.9%
(C) 11.1%
(D) 6.67%
(E) 23.6%
Rationale: Opening = 15
Closing = 16
Rise in price = 1
So, percent increase = 1/15* 100 = 6.67
Answer : D
Answer: (D) 6.67%
Question: When x is divided by 6, the quotient is y and the remainder is 1. When x is divided by 6, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?
(A) 4z/7 + 5
(B) (7z + 5) / 6
(C) (6z + 5) / 6
(D) (7z + 5) / 4
(E) (4z + 6) / 7
Rationale: When x is divided by 6, the quotient is y and the remainder is 1: x = 6y + 1.
When x is divided by 6, the quotient is z and the remainder is 6: x = 6z + 6.
Equate those two:
6y + 1 = 6z + 6;
y = (6z + 5)/6.
Answer: C.
Answer: (C) (6z + 5) / 6
Question: 892.7 – 573.07 – 95.007 = ?
(A) 224.623
(B) 224.777
(C) 233.523
(D) 414.637
(E) None of these
Rationale: Solution
Given expression = 892.7 - (573.07 + 95.007) = 892.7 - 668.077 = 224.623. Answer A
Answer: (A) 224.623
Question: What is the greatest positive integer x such that 3^x is a factor of 9^10?
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: 9^10 = (3^2)^10 = 3^20
The Answer is D. 20
Answer: (D) 20
Question: How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 8 years
(B) 4 years
(C) 3 years
(D) 9 years
(E) 5 years
Rationale: Time = (100 * 81) / (450 * 4.5)
= 4 years
Answer: B
Answer: (B) 4 years
Question: Two numbers are in the ratio of 2:3. If 20 be subtracted from each, they are in the ratio of 10:17. Find the numbers?
(A) 70,105
(B) 60,88
(C) 80,120
(D) 60,84
(E) 60,81
Rationale: (2x-20):(3x-20) =10:17
x = 35 => 70,105
Answer: A
Answer: (A) 70,105
Question: Find large number from below question The difference of two numbers is 1355. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1235
(B) 1345
(C) 1678
(D) 1767
(E) 1623
Rationale: Let the smaller number be x. Then larger number = (x + 1355).
x + 1355 = 6x + 15
5x = 1340
x = 268
Large number = 268+1355 = 1623
E
Answer: (E) 1623
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?
(A) 7.76 kms
(B) 8.76 kms
(C) 5.76 kms
(D) 3.76 kms
(E) 4.76 kms
Rationale: Explanation:
Speed in still water = 6 kmph
Stream speed = 1.2 kmph
Down stream = 7.2 kmph
Up Stream = 4.8 kmph
x/7.2 + x/4.8 = 1
x = 2.88
Total Distance = 2.88 x 2 = 5.76 kms
Answer: C
Answer: (C) 5.76 kms
Question: What least number must be subtracted from 652543 so that remaining no.is divisible by 12
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
On dividing 652543 by 12 we get the remainder 7, so 7 should be subtracted
Option C
Answer: (C) 7
Question: A, B and C have Rs.250 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) A)300
(B) B)290
(C) C)280
(D) D)270
(E) E)66
Rationale: A+B+C = 250
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 250
----------------
C = 300
Answer:A
Answer: (A) A)300
Question: Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 9^5?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 19
Rationale: 9 = 3*3= 3^2
9^5 =(3^2)^5
=3^10
we have to find the greatest positive integer value for x
when x=10, it divides exactly once and that is the least positive integer value of the quotient
therefore, the correct option is C
Answer: (C) 10
Question: Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 346
(B) 368
(C) 375
(D) 337
(E) 325
Rationale: A+B+C = 1300
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1300 => 325
Answer:E
Answer: (E) 325
Question: In how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, F, and/or G such that at least one letter is repeated within the password?
(A) 720
(B) 864
(C) 900
(D) 936
(E) 1561
Rationale: Total number of four letter passwords = 7*7*7*7= 2401 ------(1)
Total number of passwords in which no letter repeats = 7C4*4!= 35*24=840------(2)
therefore required value = (1)-(2)= 2401-840=1561
E
Answer: (E) 1561
Question: 1, 0.5, 0.5, 0.75, 1.5, ____
(A) 1.25
(B) 5.75
(C) 3.25
(D) 3.75
(E) none
Rationale: 1,0.5, 0.5, 0.75, 1.5 ,.....
1*0.5=0.5
0.5*1=0.5
0.5*1.5=0.75
0.75*2=1.5
So , 1.5*2.5=3.75
ANSWER:D
Answer: (D) 3.75
Question: In a class, the average age of 25 boys is 12 years and the average of 18 girls is 8 years. what is the average age of the whole class?
(A) 12 Years
(B) 10.3 Years
(C) 12.6 Years
(D) 13 Years
(E) 15 Years
Rationale: Total age of 43 students
(25X 12+18 X 8) = 444
Average = 444/53 = 10.3 Years
B
Answer: (B) 10.3 Years
Question: A bag contains nine black balls, three red balls and four red balls. In how many ways can two balls be drawn from the bag?
(A) ¹⁶C₂
(B) ⁹C₂
(C) ³C₂
(D) ¹²C₂
(E) ¹⁴C₂
Rationale: Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.
A
Answer: (A) ¹⁶C₂
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 99
(C) 77
(D) 66
(E) 12
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A
Answer: (A) 40
Question: The ratio between the number of sheep and the number of horses at the Stewart farm is 3 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
(A) 24
(B) 28
(C) 32
(D) 56
(E) 60
Rationale: Let the number of sheeps and horses be 3x and 7x.
Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8
Sheeps = 3x = 3*8 = 24. Hence A
Answer: (A) 24
Question: Of the teams competing in the world archery championships, Sxity percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
(A) 2/20
(B) 15/20
(C) 3/15
(D) 1/20
(E) 13/17
Rationale: Half as manymeans half of EU, then
EU 60%
US 30%
AF 5%
the rest is 5%, answer D
Answer: (D) 1/20
Question: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 600 km from the starting point ?
(A) 8 hrs 29 min
(B) 6 hrs 28 min
(C) 2 hrs 28 min
(D) 6 hrs 28 min
(E) 1 hrs 28 min
Rationale: Explanation:
Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 4 x 7 = 28 min
Hence, total time taken = 6 hrs 28 min.
Answer: D
Answer: (D) 6 hrs 28 min
Question: Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes?
(A) 1344
(B) 3360
(C) 8400
(D) 5040
(E) 67200
Rationale: 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
12 machine produce 560*6*(12/8) in 6 minutes
560*6*12/8=5040 answer is D.
Answer: (D) 5040
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (1,3), (5,3), (2,6), (6,6) ?
(A) 21.
(B) 12.
(C) 35.
(D) 49.
(E) 52.
Rationale: Delta x will give us the dimension of one side of the parallelogram = 5-1= 4 unit
Delta y will give us the dimension of the other side of parallelogram = 6-3=3 unit
Area of parallelogram = 4*3 = 12
ANSWER IS B
Answer: (B) 12.
Question: John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle?
(A) $1.63
(B) $1.64
(C) $1.68
(D) $1.73
(E) $1.76
Rationale: (1365*1.89+720*1.42)/(1365+720) =~1.73
Option (D)
Answer: (D) $1.73
Question: One week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 16 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
(A) 18
(B) 16
(C) 12
(D) 14
(E) 8
Rationale: N - Not rented trucks; R - Rented trucks
N + R = 20
N + R/2 = 16
R = 8
E
Answer: (E) 8
Question: Find the average of first 18 natural numbers.
(A) 9.5
(B) 19.5
(C) 171
(D) 18
(E) 5.9
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 18 natural numbers = (18 x 19)/2 = 171
Therefore, required average of = 171/18 = 9.5
ANSWER: A
Answer: (A) 9.5
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 87
(B) 27
(C) 70
(D) 27
(E) 20
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25
= 70.
Answer:C
Answer: (C) 70
Question: Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?
(A) 8:6
(B) 8:9
(C) 8:3
(D) 8:7
(E) 8:1
Rationale: Let the original earnings of A and B be Rs. 4x and Rs. 7x.
New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x
New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4
6x:21x/4 = 8:7
This does not give x. So, the given data is inadequate.
Answer: D
Answer: (D) 8:7
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 25%. What is the selling price of the cycle?
(A) s. 1090
(B) s. 1160
(C) s. 1190
(D) s. 1202
(E) s. 1050
Rationale: S.P. = 75% of Rs. 1400 = Rs.75/100x 1400	= Rs. 1050
ANSWER :E
Answer: (E) s. 1050
Question: A set of books costs the merchant $500. At what price would the merchant be sold the set of books if he got loss of 5% ?
(A) $475
(B) $480
(C) $485
(D) $495
(E) None of these
Rationale: Cost Price = $500
Loss % = 5
Selling Price = ?
Selling Price = (100 - loss %) * Cost Price /100
= (100 - 5) * 500 / 100
= 475
Answer is A
Answer: (A) $475
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
(A) 1365
(B) 1500
(C) 1406
(D) 1879
(E) 2000
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
ANSWER A
Answer: (A) 1365
Question: A train running at the speed of 180 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150 meter
(B) 286 meter
(C) 186 meter
(D) 288 meter
(E) 450 meter
Rationale: Speed = 180*(5/18) m/sec
= 50 m/sec
Length of Train (Distance)
= Speed * Time
(50) * 9 = 450 meter
Answer:E
Answer: (E) 450 meter
Question: In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What isthe probability that theextracted ball would turn on to be white, if all possible hypothesis concerning the color of the balls that initially in the bag were equally possible ?
(A) 2/3
(B) 5/8
(C) 3/5
(D) 4/7
(E) 5/8
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8
Question: A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
(A) 18 days
(B) 24 days
(C) 30 days
(D) 36 days
(E) 35 days
Rationale: Explanation:
2(A + B + C)'s 1 day's work =(1/30 +1/24+1/20)=15/120=1/8
Work done by A, B, C in 10 days =10/6=5/8.
A's 1 day's work =(1/16 - 1/24)=1/48
Now,	1/48 work is done by A in 1 day
So,	3/8 work will be done by A in (48 X 3/8)= 18 days.
ANSWER IS A
Answer: (A) 18 days
Question: A man in a train travelling at 25km/hr notices that a train going in the opposite direction passes him in 7 sec.If the length of this train is 180m find its speed .
(A) 30 km/hr
(B) 40 km/hr
(C) 50 km/hr
(D) 68 km/hr
(E) 70 km/hr
Rationale: relative speed of trains = 180/7 mtrs/sec = 180*18/(7*5)= 93 km/hr
speed of 2nd train = 93-25=68 km/hr
ANSWER:D
Answer: (D) 68 km/hr
Question: 7 persons a, b, c, d, e, f and g are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
(A) 24
(B) 36
(C) 480
(D) 720
(E) 2880
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 7 are there..
take a,b, and c as one,so total =5..
these 5 can be arranged in 5! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 5!*3!=720
D
Answer: (D) 720
Question: A student is mixing oil and water as part of an experiment. The student's mixture has a 5:3 oil to water ratio. If the student used 12 more units of oil than water, how many units of water were used?
(A) 14
(B) 18
(C) 19
(D) 22
(E) 24
Rationale: Let 5u and 3u be the units of oil and water, respectively
5u - 3u = 12
2u = 12 => u = 6
Water => 3u = 18
Answer: B
Answer: (B) 18
Question: The number of the members of a club is more than 20 and less than 50. When 4 people sit at a table, other people exactly divided to 6-people groups (6 people sit at a table) or 7-people groups (7 people sit at a table). If the members are divided to 8-people groups, how many people will be left?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The number of members is 7k+4 = 6j+4
The only number in this range which satisfies this is 46.
46/8 = 5(8) + 6
The answer is D.
Answer: (D) 6
Question: If the sum of two numbers is 18 and the sum of their squares is 180, then the product of the numbers is
(A) 72
(B) 44
(C) 80
(D) 88
(E) 48
Rationale: according to the given conditions x+y = 18
and x^2+y^2 = 180
now (x+y)^2 = x^2+y^2+2xy
so 18^2 = 180 + 2xy
so xy = 144/2 = 72
ANSWER:A
Answer: (A) 72
Question: A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 4
(B) 5
(C) 3
(D) 2
(E) 8
Rationale: M = 12
S = x
DS = 12 + x
US = 12 - x
12 + x = (12 - x)2
12 + x = 24 -2x
3x = 24
x = 4
Answer:A
Answer: (A) 4
Question: In a container of vegetables there are 25% potatoes, 40% onions and the rest are tomatoes. If there are 200 kgs vegetables in the container, how many tomatoes are there in the container?
(A) 70 kg
(B) 58 kg
(C) 110 kg
(D) 85 kg
(E) 65 kg
Rationale: Explanation :
100% of Vegetables = 200 kgs
Tomatos = 100% (25% + 40%) = 100% 65% = 35%
Therefore 35% = 200 X 35/100 = 70 Kgs
Answer : A
Answer: (A) 70 kg
Question: The cost of 8 gel pens and 12 ball pens is Rs.82. What would be the cost of 36 gel pens and 54 ball pens?
(A) Rs.366
(B) Rs.365
(C) Rs.369
(D) Rs.364
(E) None of these
Rationale: Explanation:
From the given statement we have,
The cost of 4 gel pens + 6 ball pens = Rs.41.
Multiplying each terms by 9, we get
The cost of 36 gel pens + 54 ball pens = Rs.369
Answer: Option C
Answer: (C) Rs.369
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 3/16
(B) 3/28
(C) 3/11
(D) 3/19
(E) 3/29
Rationale: The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
Answer:C
Answer: (C) 3/11