mathewhe/aqua_rat huggingface dataset:
Question: A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
(A) 76 hrs
(B) 99 hrs
(C) 55 hrs
(D) 90 hrs
(E) 11 hrs
Rationale: 1/9 - 1/x = 1/10
=> 90 hrs
Answer: D
Answer: (D) 90 hrs
Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 48 lots are to have 100 feet of frontage each, what is the value of x ?
(A) 5,280
(B) 3,200
(C) 3,700
(D) 4,400
(E) 4,760
Rationale: Total number of plots,be T
Plots with 80ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 48 T = 54
Total lake frontage = 48X100 + 6X80 = 5280
Answer : A
Answer: (A) 5,280
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 299
(B) 277
(C) 276
(D) 270
(E) 281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: (D) 270
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 42 as quotient. What is the correct quotient ?
(A) 0
(B) 12
(C) 13
(D) 20
(E) 24
Rationale: 12*42=504
504%21=24
ANSWER:E
Answer: (E) 24
Question: The ratio between the speeds of two trains is 3 : 8. If the second train runs 600 kms in 6 hours, then the speed of the first train is
(A) 37.5 km/h
(B) 60.5 km/h
(C) 42.5 km/h
(D) 32.5 km/h
(E) 35.5 km/h
Rationale: A
37.5 km/h
Answer: (A) 37.5 km/h
Question: How many prime numbers exist in 67 x 353 x 1110 ?
(A) 30 prime number
(B) 29 prime number
(C) 27 prime number
(D) 31 prime number
(E) None of these
Rationale: Solution:
=(2 x 3)7 x (5 x 7)3 x 1110
=27 x 37 x 53 x 73 x 1110
Thus, there are (7 + 7 + 3 + 3 + 10) = 30 prime number
ANSWER:A
Answer: (A) 30 prime number
Question: A car owner buys petrol at 7.50, 8.00 and 8.50 per litre for three successive years. What approximately is his average cost per litre of petrol if he spends 4000 each year?
(A) 8
(B) 9
(C) 7.98
(D) 7.98
(E) None of the above
Rationale: Let average cost of petrol per litre be x
Then x = 12000 /4000/7.5+4000/8+4000/8.5
= 3 /2/15+1/8+2/17=6120/767= Rs. 7.98 per litre
Answer C
Answer: (C) 7.98
Question: What least number should be added to 1022, so that the sum is completely divisible by 25?
(A) 4
(B) 3
(C) 2
(D) 0
(E) 5
Rationale: 1022 Ã· 25 = 40 with remainder = 22
22 + 3 = 25.
Hence 3 should be added to 1022 so that the sum will be divisible by 25
Answer: Option B
Answer: (B) 3
Question: Indu gave Bindu Rs.2500 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 2% per annum simple interest?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 2500 = D(100/2)2
D = 1
Answer: A
Answer: (A) 1
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 9
(A) 1/2
(B) 7/18
(C) 5/13
(D) 5/12
(E) 6/17
Rationale: Total number of cases = 8*8 = 64
Favourable cases = [(2,8),(3,6),(3,7),(4,6),(4,7),(4,8),(5,5),(5,6),(5,7),(5,8),(6,4),(6,5),(6,6),(6,7),(6,8),(7,3),(7,4),(7,5),(7,6),(7,7),(7,8),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(8,8)] = 28
So Probability = 28/64 = 7/18
Answer is B
Answer: (B) 7/18
Question: If 'x' is a positive integer exactly divisible by 6 or 15 but not divisible by 12.What could possibly be the value of 'x' ?
(A) 120
(B) 60
(C) 36
(D) 90
(E) 54
Rationale: 120 and 60 are both divisible by 6 and 15 but also by 12. so they are not the right answer.
36 and 54 are both clearly not divisible by 15(not correct)
90 is both divisible by 6 and 15 but not by 12.
answer : (D) 90
Answer: (D) 90
Question: The ration between the present ages of P and Q is 6:7. If Q is 4 years older than P, what will be the ratio of the ages of P and Q after 4 years?
(A) 2:3
(B) 7:8
(C) 11:13
(D) 9:13
(E) 1:2
Rationale: Let P's and Q's age be 6x and 7x
7x-6x = 4
x = 4
Required ratio = (6x+4):(7x+4) = 28:32 = 7:8
Answer is B
Answer: (B) 7:8
Question: How many R ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?
(A) 120
(B) 240
(C) 360
(D) 540
(E) 720
Rationale: Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways R=> 2*5*4*3*2*1 = 240.B
Answer: (B) 240
Question: The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
(A) Rs. 8400
(B) Rs. 8721
(C) Rs. 8856
(D) Rs. 9000
(E) None of these
Rationale: Explanation:
Actual price = 95% of 90% of 85% of Rs. 12000
= 95/100 * 90/100 * 85/100 * 12000 = Rs. 8721.
ANSWER IS B
Answer: (B) Rs. 8721
Question: If s is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 12
Rationale: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey s=4n, if it really wanted to convey so.
From other questions that I have seen, proper wordings could be:
If s is three times as large as n
OR simply,
If s is three times n.C
Answer: (C) 3
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.68?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 8
Rationale: for the 1st no. there are 2 digits after decimal
for the 2nd no. there are 2 digits after decimal
total no. of decimals = 4
req. no. of digits=(n-1)=(4-1)=3
ANSWER :D
Answer: (D) 3
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) 1410
(B) 1420
(C) 1360
(D) 1440
(E) 1540
Rationale: S.P. = 85% of Rs. 1600 = 85/100 x1600= Rs. 1360
answer : C
Answer: (C) 1360
Question: The average earning of amechanic for the first 4days of a week is Rs.53 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
(A) s. 10
(B) s. 20
(C) s. 30
(D) s. 40
(E) s. 50
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 53 + 4 x 22 -20
= Rs. 280
âˆ´ Average earning = 280/ 7
= Rs. 40
D
Answer: (D) s. 40
Question: A certain collage has total of 410 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
(A) 60
(B) 90
(C) 70
(D) 80
(E) 40
Rationale: Answer is B.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 410 seniors.
So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f =90.
B
Answer: (B) 90
Question: The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 3:5
(B) 3:9
(C) 3:2
(D) 2:2
(E) 3:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/15
= (1)^2h1/(2)^2h2
=> h1/h2 = 3/5
i.e. h1 : h2 = 3:5
Answer: A
Answer: (A) 3:5
Question: What is the smallest no. which must be added to 27452 so as to obtain a sum which is divisible by 9?
(A) 7
(B) 2
(C) 9
(D) 4
(E) 6
Rationale: For 27452 , 2+7+4+5+2=20.
7 must be added to 27452 to make it divisible by 9.
Now , 2+7+4+5+9=27 => 27 is a multiple of 9 and hence 27452 is also divisible by 9
A
Answer: (A) 7
Question: The monthly rent of a shop of dimension 10feet × 10feet is Rs.1300. What is the annual rent per square foot of the shop?
(A) 43
(B) 156
(C) 68
(D) 87
(E) 92
Rationale: Sol. Monthly rent per square feet = 1300/(10*10) = 13
& Annual rent per square feet
=12*13=156
Answer : B
Answer: (B) 156
Question: For every integer n ≥ 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(102) – h(101)?
(A) 102
(B) 0
(C) 101
(D) 98
(E) 100
Rationale: h(101) = 1*3*5*7*9*...*99*101
h(102) = 1*3*5*7*9*...*99*101
They are going to be the same. Hence their difference will be 0
hence:B
Answer: (B) 0
Question: A boy swims downstream 48 km and upstream 12 km taking 6 hours each time; what is the speed of the current?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 48 --- 6 DS = 8
? ---- 1
12 ---- 6 US = 2
? ---- 1 S = ?
S = (8 - 2)/2 = 3
Answer: C
Answer: (C) 3
Question: Which of the following integers has the most number of divisors?
(A) 176
(B) 182
(C) 99
(D) 101
(E) 102
Rationale: Explanation:
99 = 1 × 3 × 3 × 11
=> Divisors of 99 are 1, 3, 11, 9, 33 and 99
101 = 1 × 101
=> Divisors of 101 are 1 and 101
182 = 1 × 2 × 7 × 13
=> Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182
176 = 1 × 2 × 2 × 2 × 2 × 11
=> Divisors of 176 are 1, 2, 11, 4, 22, 8, 44, 16, 88, 176
Hence 176 has most number of divisors.
Answer: Option A
Answer: (A) 176
Question: In western Europe, C bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?
(A) 9% of (x/100)
(B) 14% of (x/100)
(C) 75% of (x/100)
(D) 9% of x
(E) 14% of x
Rationale: Moreover is't question actually asking the the difference between the {(Quantity Produced + Quantity Sold ) C in 1990 - (Quantity Produced + Quantity Sold ) in 1993}
Though the Quantity sold in both the years is same it actually boils down to (Quantity Produced in 1990 ) in (Quantity Produced in 1993)=D
Answer: (D) 9% of x
Question: In what ratio must tea at Rs. 62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be worth Rs. 64.50 per Kg?
(A) 3 :1
(B) 2:1
(C) 4:1
(D) 1:3
(E) 1:2
Rationale: C.P of a unit quantity of 1st kind = Rs. 62
C.P of a unit quantity of 2nd kind = Rs. 72
Mean price = Rs. 64.50
C.P of a unit quantity of 1st kind - Mean price =64.50-62= 2.50
C.P of a unit quantity of 2nd kind - Mean price = 72-64.50 =7.50
Required ratio = 7.50 : 2.50 = 3 : 1
Answer:A
Answer: (A) 3 :1
Question: During a Thanksgiving weekend, a car rental company rented eight-tenths of their vehicles, including three-fifths of the 4WDs that it had. If 40% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
(A) 20%
(B) 30%
(C) 40%
(D) 60%
(E) 25%
Rationale: 2/10 of all the vehicles were not rented.
(2/5)(2/5) = 4/25 of all the vehicles are 4WDs that were not rented.
(4/25) / (2/10) = 4/5 is the fraction of non-rented vehicles that were 4WDs
1 - 4/5 = 20% of non-rented vehicles were not 4WDs.
The answer is A.
Answer: (A) 20%
Question: The greatest number that divides 690 and 875 leaving remainders 10 and 25 respectively is:
(A) 170
(B) 130
(C) 150
(D) 120
(E) 180
Rationale: Explanation:
690 -10= 680, 875 – 25 = 850
Highest number that can divide 680 and 850 exactly is HCM of the numbers.
HCF of 680 and 850 = 170
Answer:A
Answer: (A) 170
Question: In a simultaneous throw of 2 dice, what is the probability of getting a total of 10 or 11?
(A) 2/7
(B) 1/4
(C) 1/2
(D) 7/36
(E) 5/36
Rationale: n(S) = 6*6 = 36
E = event of getting a total of 10 or 11 = {(4,6),(5,5),(6,4),(5,6),(6,5)}
probability = 5/36
Answer is E
Answer: (E) 5/36
Question: If a person walks at 14 miles/hr instead of 10 miles/hr, he would have walked 20 miles more. The actual distance traveled by him is:
(A) 20 miles
(B) 50 miles
(C) 30 miles
(D) 25 miles
(E) 35 miles
Rationale: Let the actual distance traveled be x km.
Then, X/10 = (X + 20)/14 ==> 14X = 10X + 200 ==> 4X = 200
X = 50.
Answer B) 50 miles.
Answer: (B) 50 miles
Question: The first five numbers in a regular sequence are 4, 11, 25, 53, and 109. What is the next number in the sequence?
(A) 142
(B) 221
(C) 176
(D) 182
(E) 190
Rationale: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..
when we see the sequence 4, 11, 25, 53, and 109, we see that each succeeding number is some value more than twice the previous number..
10=2*4+3..
22=2*10+3..
and so on..
so next number= 2*109+3=221..
B
Answer: (B) 221
Question: A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to
(A) 20
(B) 5
(C) 30
(D) 35
(E) 67
Rationale: Explanation :
Total no of characters= 20 * 55 * 65.
From the problem it is clear that 20 * 55 * 65 = x * 65 * 70.
we get x= 15.6 ∼ 16 because these are sheets.
therefore 4 less sheets.
Hencde, there is 20% decrease in number of sheets.
Answer : A
Answer: (A) 20
Question: How many seconds will a 800 m long train take to cross a man walking with a speed of 5 km/hr in the direction of the moving train if the speed of the train is 65 km/hr?
(A) 30
(B) 50
(C) 66
(D) 44
(E) 48
Rationale: Speed of train relative to man = 65-5= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 800 * 3/50 = 48 sec.
Answer: E
Answer: (E) 48
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
(A) 700
(B) 720
(C) 800
(D) 820
(E) 830
Rationale: Option 'B'
Answer: (B) 720
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is?
(A) 625
(B) 827
(C) 657
(D) 726
(E) 634
Rationale: Let the sum be Rs. x. Then,
[x (1 + 4/100)2 - x] = (676/625 x - x)
= 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x
= 625.
Answer: A
Answer: (A) 625
Question: In a certain city, 70 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:
(A) 45,000 to 90,000 inclusive
(B) 30,000 to 120,000 inclusive
(C) 60,000 to 90,000 inclusive
(D) 60,000 to 120,000 inclusive
(E) 90,000 to 120,000 inclusive
Rationale: The maximum percentage with both is 60% which is 90,000 households.
This means that every household with a recorder also has cable television.
The minimum percentage with both is 30% which is 45,000 households.
This means that 30% of households have only recorders but not cable television.
The other 30% of households with recorders have cable television.
The answer is A.
Answer: (A) 45,000 to 90,000 inclusive
Question: A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 210 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
(A) 5 mph
(B) 10 mph
(C) 20 mph
(D) 30 mph
(E) 40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Day 1 time = T1
Day 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Day 1 Rate = R1
Day 2 Rate = R2
R1 - R2 = 10 mph
i.e. R1 = 10 + R2
280 = 8R2 + 4R1
i.e. 280 = 8R2 + 4 (10 + R2)
i.e. R2 = 20 mph
ANSWER: D
Answer: (D) 30 mph
Question: If 853,845 bars of chocolate need to be placed in little boxes and each box can contain at most 9 bars of chocolate. How many bars of chocolate will be in the last unfilled box?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: The number of bars of chocolate that can be placed in the little boxes of 9 bars is the first number that is divisible by 9 that occurs before 853,845.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 853,845 = 33 and 27 is divisible by 9.
Hence, we need to remove 6 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) 6
Question: For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,3), what are the coordinates of the remaining vertex?
(A) (3,4)
(B) (3,9)
(C) (4,9)
(D) (6,4)
(E) (9,6)
Rationale: Let (a,b) be the remaining vertex.
x: 0 + 6 + a = 3*3. Then a = 3.
y: 0 + 0 + b = 3*3. Then b = 9.
The answer is B.
Answer: (B) (3,9)
Question: If st = 3(s+ 1) + t and s and t are integers, s could be any of the following values EXCEPT:
(A) 2
(B) 4
(C) 10
(D) 3
(E) 7
Rationale: st = 3(s + 1) + t
st - q = 3(s + 1)
t = 3(s + 1)/(s-1)
t won't be an integer only if s = 10 (from the options).
Answer: E
Answer: (E) 7
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 65
(B) 77
(C) 24
(D) 71
(E) 27
Rationale: Explanation:
B = 1/8 â€“ 1/2 = 1/24 => 24 days
Answer:C
Answer: (C) 24
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 729 more than 4times the middle integer. Find the numbers?
(A) 650
(B) 678
(C) 698
(D) 710
(E) 729
Rationale: x + 4 (x + 4) = 729 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 729 + 4 x + 8
x = 721
x + 2 = 723
x + 4 = 725
Check: the smallest is added to four times the largest
721 + 4 * 725 = 3621
four times the middle
4 * 723 = 2892
3621 is more than 2892 by
3621 - 2892 = 729
E
Answer: (E) 729
Question: Find the sum of all 4 digit numbers formed using digits 1,2,5,6.
(A) 93324
(B) 92324
(C) 93424
(D) 93424
(E) 93824
Rationale: (n-1)! * (111...n) *(sum of the digits)
=(4-1)!*1111*(1+2+5+6)
=93324
ANSWER:A
Answer: (A) 93324
Question: Excluding stoppages, the speed of a bus is 65 kmph and including stoppages, it is 48 kmph. For how many minutes does the bus stop per hour?
(A) 70 min
(B) 15 min
(C) 20.4 min
(D) 15.6 min
(E) 40 min
Rationale: D
15.6 min
Due to stoppages, it covers 17 km less.
Time taken to cover 17 km = (17/65 x 60) min = 15.6 min
Answer: (D) 15.6 min
Question: If pqr = 0 , qrs = 0 , and spr = 1, which of the following must be zero?
(A) P
(B) Q
(C) R
(D) S
(E) T
Rationale: prs = 1 which means neither p / r/s is 0
rsx q = 0 , we know r and s are is not 0 from above hence q must be 0.
q x p x r = 0, we know from first expression that p and r are not 0 hence q =0.
option B
Answer: (B) Q
Question: The average weight of 8 persons increases by 1.5kg when a person weighting 65kg is replaced by a new person. What could be the weight of the new person?
(A) 67kg
(B) 77kg
(C) 87kg
(D) 97kg
(E) None of these
Rationale: Explanation:
Let the average weight of 8 persons be ‘x’
years and the age of the new person be ‘y’ years
so, (8x – 65 + y) / 8 = x+1.5
so, y = 77kgs
65 + 8X1.5 = 77kgs
Answer B
Answer: (B) 77kg
Question: In how many ways can the letters of the word FINISHED be arranged?
(A) 20155
(B) 1643
(C) 2520
(D) 20152
(E) 20160
Rationale: FINISHED has 8 words, but I is repeated two times. Thus ways = 8! / 2! = 20160 ways
E
Answer: (E) 20160
Question: If xy = 3(x + 1) + y and x and y are integers, x could be any of the following values EXCEPT:
(A) 2
(B) 8
(C) 4
(D) 3
(E) 7
Rationale: xy = 3(x + 1) + y
xy - y = 3(x + 1)
y = 3(x + 1)/(x-1)
y won't be an integer only if x = 8 (from the options).
Answer: B
Answer: (B) 8
Question: If x is negative and y is positive, which of the following cannot be positive?
(A) x/y
(B) -x*y
(C) -x/y
(D) x^2+y
(E) x^6+y
Rationale: - /+ = -
x/y is negative.
Answer : A
Answer: (A) x/y
Question: A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of :
(A) 45 hours
(B) 47 hours
(C) 48 hours
(D) 50 hours
(E) None
Rationale: Explanation:
Basic rate per hour = Rs.(20/40)= Rs.1/2
Overtime per hour = 125% of Rs.1/2=125/100×1/2=Rs.5/8
Suppose he worked x hours overtime.
Then,20+5/8x=25 or 5/8x=5
x=5×8/5=8 hours
So he worked in all for (40+8) hours = 48 hours.
Correct Option: C
Answer: (C) 48 hours
Question: A certain auto manufacturer sold 6% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.6 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 17,00,000
(B) 18,00,000
(C) 20,00,000
(D) 25,00,000
(E) 26,00,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-6/100(X)
If sales in 2006,X= 2.6 million find X-6/100(X)
(2.6 x 10^6)-6/100(2.6 x 10^6)
2600000-1,56,000=24,44,000-----> 25,00,000(approx)
Answer-D
Answer: (D) 25,00,000
Question: Marketing executives for a certain chewing gum company projected a 40 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 30%. What percent of the projected revenue was the actual revenue ?
(A) 50%
(B) 58%
(C) 62.5%
(D) 64%
(E) 75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 70;
Projected revenue = 140.
Actual/Projected*100=70/140*100 = 50%.
Answer: A.
Answer: (A) 50%
Question: A die is rolled twice. What is the probability of getting a sum equal to 12?
(A) 1/36
(B) 1/9
(C) 1/7
(D) 1/24
(E) 2/36
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 12 when the two dice fall = {(6, 6)}
Hence, n(E) = 1
P(E) = n(E)/n(S)
=1/36
=1/36
Answer : Option A
Answer: (A) 1/36
Question: A shoe shop sells four different brands of shoes( brand A, B,C and D),
I) brand A cost 5% less than brand B
II) brand C cost 15% less than brand A
III) brand D cost 10% less than brand C
what percent of brand B's cost is brand D?
(A) 70.5%
(B) 62.2%
(C) 60.9%
(D) 62.5%
(E) 72.9%
Rationale: Let the cost of brand B be $100
I) brand A cost 5% less than brand B--100-5=95
II) brand C cost 15% less than brand A--95-13.95=81.05
III) brand D cost 10% less than brand C--81.05-8.105=72.945
what percent of brand B's cost is brand D=72.945*100/100
Answer is E
Answer: (E) 72.9%
Question: (2.3)(0.001)(2.2)(0.01)=?
(A) 0.000506
(B) 0.00506
(C) 5.06e-05
(D) 0.506
(E) 5.06e-07
Rationale: Divide the four terms into two,(2.3)(0.001)*(2.2)(0.01).
2.3*0.001 gives a value 0.0023 and 2.2*0.01 gives 0.022(remember that the place value should be placed carefully)
0.0023*0.022 = multiply 23 and 22 gives 506.. the number of digits could be move 7 places..
so, the answer will be 0.0000506
The answer is option C
Answer: (C) 5.06e-05
Question: A man can row his boat with the stream at 6 km/h and against the stream in 3 km/h. The man's rate is?
(A) 1.5 kmph
(B) 4 kmph
(C) 5 kmph
(D) 7 kmph
(E) 8 kmph
Rationale: DS = 6
US = 3
S = ?
S = (6 - 3)/2 = 1.5 kmph
Answer: A
Answer: (A) 1.5 kmph
Question: The average (arithmetic mean) of four numbers is 5x + 3. If one of the numbers is 2x, what is the average of the other three numbers?
(A) x + 1
(B) 3x + 3
(C) 4x + 1
(D) 5x + 3
(E) 6x + 4
Rationale: The sum of all four numbers is 4 * (5x + 3) = 20x + 12.
If one of the numbers is 2x, the sum of the other 3 numbers is 18x+12.
The average of the remaining three numbers is (18x+12)/3 = 6x+4.
The answer is E.
Answer: (E) 6x + 4
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 1000 m long?
(A) 220 Sec
(B) 190 Sec
(C) 167 Sec
(D) 197 Sec
(E) 179 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2200 m
T = D/S
T = 2200/10
T = 220 Sec
Answer: A
Answer: (A) 220 Sec