mathewhe/aqua_rat huggingface dataset:
Question: A boy has Rs. 560 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) 90
(B) 105
(C) 140
(D) 130
(E) 120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 560
16x = 560
x = 35.
Hence, total number of notes = 3x = 105.
B
Answer: (B) 105
Question: A group of men decided to do a work in 17 days, but 8 of them became absent. If the rest of the group did the work in 21days, Find the original number of men?
(A) 15
(B) 20
(C) 42
(D) 25
(E) 18
Rationale: Original number of men = 8*21 / (21-17) = 42
Answer is C
Answer: (C) 42
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 50% are drinking beer, 20% are drinking mixed drinks, and 30% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
(A) 1
(B) 4/7
(C) 10/19
(D) 7/24
(E) 7/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
50% drink beer = 20
30% mixed = 12
20% both = 8
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 20+18 =38 and both = 20
thus 20/38 = 10/19
Hence C
Answer: (C) 10/19
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) 4082.89
(B) 4082.49
(C) 4082.477
(D) 4082.4
(E) 4082.41
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6
= Rs.4082.40
Answer: D
Answer: (D) 4082.4
Question: A train covers a distance of 20 km in 30 min. If it takes 18 sec to pass a telegraph post, then the length of the train is?
(A) 298 m
(B) 125m
(C) 120 m
(D) 217 m
(E) 200 m
Rationale: Speed = (20/30 * 60) km/hr
= (40 * 5/18) m/sec
= 100/9 m/sec.
Length of the train
= 100/9 * 18
= 200 m.
Answer: E
Answer: (E) 200 m
Question: A man swims downstream 100 km and upstream 30 km taking 10 hours each time; what is the speed of the current?
(A) 2.5
(B) 3.5
(C) 4.5
(D) 5.3
(E) 3.4
Rationale: 100 --- 10 DS = 10
? ---- 1
30 ---- 10 US = 3
? ---- 1 S = ?
S = (10 - 3)/2 = 3.5
Answer: B
Answer: (B) 3.5
Question: In what ratio must rice of Rs.54per kg be mixed with rice of Rs.35 per kg so that cost of mixture is Rs.42 per kg?
(A) 9:7
(B) 7:12
(C) 12:7
(D) 5:6
(E) 7:9
Rationale: (42-35)/(54-42)=7/12=7:12
ANSWER:B
Answer: (B) 7:12
Question: Find the area of circle whose radius is 3m?
(A) 18.57
(B) 15.84
(C) 17.27
(D) 28.28
(E) 29.88
Rationale: 22/7 * 3 * 3
= 28.28
Answer:D
Answer: (D) 28.28
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 20
(B) 16
(C) 24
(D) 28
(E) 21
Rationale: Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
Answer:E
Answer: (E) 21
Question: total dinning bill of 9 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
(A) 21.84
(B) 12.84
(C) 16.98
(D) 24.84
(E) 15.84
Rationale: dinner bill of 9 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/9 = $ 16.98
ANSWER:C
Answer: (C) 16.98
Question: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 18 sec
(B) 20 sec
(C) 76 sec
(D) 15 sec
(E) 17 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
Answer:B
Answer: (B) 20 sec
Question: Can X and can В are both right circular cylinders. The radius of can X is twice the radius of can B, while the height of can X is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can X with the same brand of gasoline?
(A)  $1
(B)  $2
(C)  $4
(D)  $8
(E)  $16
Rationale: Let x be the radius of b and 2h be the height of B. Therefore, radius of X = 2x and height = h
Vol of b = 3.14*x^2*2h
Vol of a = 3.14*4x^2*h
cost to fill half of B = $4 --> cost to fill full B = $8
--> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16
Ans E
Answer: (E)  $16
Question: The ages of two persons differ by 16 years. 3 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
(A) 15
(B) 20
(C) 25
(D) 27
(E) 35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 3) = 3 (x-16-3)
=> x � 3 = 3x � 57
=> 2x = 54
=> x = 54/2 = 27
Answer: Option D
Answer: (D) 27
Question: A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in
(A) 18 sec
(B) 12 sec
(C) 15 sec
(D) 20 sec
(E) 13.5 sec
Rationale: Length of train = 12 Ã— 15 = 180 m.
Then, speed of train = 180â„18 = 10 m/s
Now, length of train = 9 Ã— 15 = 135m
âˆ´ Required time = 135â„10 = 13.5 sec.
Answer E
Answer: (E) 13.5 sec
Question: What is the volume of a cube?
I. The area of each face of the cube is 64 square metres.
II. The length of one side of the cube is 8 metres.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
Let each edge be a metres. Then,
I. a2 = 64 a = 8 m Volume = (8 x 8 x 8) m3 = 512 m3.
Thus, I alone gives the answer.
II. a = 8 m Volume = (8 x 8 x 8) m3 = 512 m3.
Thus, II alone gives the answer.
Correct answer is (C).
Answer: (C) Either I or II alone sufficient to answer
Question: Ajit opened a shop investing Rs. 30000. Sujeet joined him 2 months later, investing Rs. 45000. They earned a profit of Rs. 54000 after completion of one year. What will be Sujeet's share of profit ?
(A) 27000
(B) 24000
(C) 30000
(D) 36000
(E) None of these
Rationale: Explanation :
Ajit : Sujeet = 30000*12 : 45000*10 = 4 : 5.
Sujeet's share = Rs. 54000 * (5/9) = Rs. 30000.
Answer : C
Answer: (C) 30000
Question: Insert the missing number.
2, 6, 12, 20, 30, 42, 56, 72, 90 (....)
(A) 110
(B) 38
(C) 72
(D) 66
(E) 19
Rationale: Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8,8 x 9, 9 x 10.
So, the next number is 10 x 11 = 110.
Answer: A) 110
Answer: (A) 110
Question: A train 700 meters long is running with a speed of 50 kmph. The time taken by it to cross a tunnel 160 meters long is?
(A) 29
(B) 18
(C) 48
(D) 62
(E) 11
Rationale: D = 700 + 160 = 860
S = 50 * 5/18 = 13.89 mps
T = 860/13.89 = 62 sec
Answer: D
Answer: (D) 62
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 16 seconds
(B) 15 seconds
(C) 14 seconds
(D) 12 seconds
(E) 13 seconds
Rationale: Speed of the boat downstream = 15 + 3
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:D
Answer: (D) 12 seconds
Question: If the average (arithmetic mean) of seven consecutive integers is 20, then the product of the greatest and least integer is
(A) 343
(B) 393
(C) 363
(D) 391
(E) 409
Rationale: n = smallest number
n+6 = largest number
(n + n + 6)/2 = 20
=> (2n+6)/2 = 20
=> n + 3 = 20
=> n = 17
So Product of n and n+6 = (17) (23)
= 391
Answer - D
Answer: (D) 391
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 9?
(A) a. 220
(B) b. 249
(C) c. 432
(D) d. 216
(E) e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 432
ANSWER OPTION E
Answer: (E) e. 288
Question: A sum fetched a total simple interest of 4034.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
(A) 5768
(B) 8925
(C) 8965
(D) 6474
(E) 8723
Rationale: Principal = (100 x 4034.25)/(9 x 5)
= 403425/45
= 8965.
ANSWER C
Answer: (C) 8965
Question: The average of six numbers is 3.95. The average of two of them is 3.6, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(A) 4.4
(B) 4.6
(C) 4.7
(D) 4.8
(E) 4.9
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.6 × 2) + (3.85 × 2)]
= 23.70 – (7.2 + 7.7)
= 23.70 – 14.9 = 8.80
∴ Required average = (8.8⁄2) = 4.4
Answer A
Answer: (A) 4.4
Question: In how many different ways can the letters of the word "CORPORATION" be arranged in such a way that no two vowels are together?
(A) 6!/2!∗C57∗5!3!
(B) 4!/2!∗C57∗5!3!
(C) 6!/2!∗C57∗6!3!
(D) 3!/2!∗C57∗5!3!
(E) 12!/2!∗C57∗5!3!
Rationale: Step 1: Separate consonants with 7 empty slots *C*R*P*R*T*N*.
Step 2: 6 consonants CRPRTN can be arranged in 6!/2! ways (6 letters with two R's);
Step 3: we have 5 vowels OOAIO. Choose 5 slots out of 7 for them (this way no two vowels will be together): C57
Step 4: 5 vowels in their slots can be arranged in 5!/3! ways (5 letters with three O's).
Total = 6!/2!∗C57∗5!3!
Answer: A
Answer: (A) 6!/2!∗C57∗5!3!
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:00 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 10.18 p.m
(B) 10.29 p.m
(C) 10.00 p.m
(D) 10.38 p.m
(E) 10.32 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.00 + 7 h = 10.00 p.m.
Answer:C
Answer: (C) 10.00 p.m
Question: Kingfisher company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
(A)  3,024
(B)  4,536
(C)  5,040
(D)  9,000
(E)  10,000
Rationale: Kingfisher company plans to assign identification numbers to its employees.The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.
Total = 9*9*8*7 = something with the units digit if 6.
Answer: B.
Answer: (B)  4,536
Question: Length of a rectangular plot is 16 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 58 m
(B) 60 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let breadth = x metres.
Then, length = (x + 16) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 16) + x] = 200
2x + 16 = 100
2x = 84
x = 42.
Hence, length = x + 16 = 58 m
A
Answer: (A) 58 m
Question: What is the smallest number which when increased by 7 is divisible by 25, 49, 15, and 21?
(A) 3,551
(B) 3,668
(C) 3,733
(D) 3,822
(E) 3,957
Rationale: First factor each of 25, 49, 15, and 21 into primes:
25=5*5; 49=7*7; 15=3*5; 21=3*7
the smallest number divisible by each of the numbers is 3*5*5*7*7 = 3,675
3,675-7 = 3,668 thus 3,668 + 7 is the smallest number divisible by 25, 49, 15, and 21
B
Answer: (B) 3,668
Question: The reciprocal of the hcf and lcm of two are 1/16 and 1/312 .if one of the number is 24 then other no. is
(A) 126
(B) 136
(C) 146
(D) 208
(E) 266
Rationale: reciprocal of the hcf and lcm of two are 1/16 and 1/312
so, HCF = 16 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 16*312 / 24 = 208
ANSWER:D
Answer: (D) 208
Question: A sum of money deposited at C.I. amounts to Rs.3650 in 2 years and to Rs.4015 in 3 years. Find the rate percent?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Explanation:
3650 -------- 365
100 -------- ? (10%)
Answer: Option A
Answer: (A) 10%
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 80
(B) 85
(C) 96
(D) 125
(E) 200
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
ANSWER C
Answer: (C) 96
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold $390 kilograms of pears that day, how many kilograms did he sell in the afternoon?
(A) 120
(B) 180
(C) 260
(D) 280
(E) 320
Rationale: 3x=390
x=130
Therefore, the salesman sold 130kg in the morning and 2⋅130=260 kg in the afternoon. So answer is C.
Answer: (C) 260
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?
(A) 22
(B) 77
(C) 32
(D) 27
(E) 29
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer: C
Answer: (C) 32
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 2
Rationale: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Answer: A
Answer: (A) 9
Question: When positive integer x is divided by 9, the quotient is y and the remainder is 4. When 2x is divided by 7, the quotient is 2y and the remainder is 1. What is the value of 5y – x?
(A) -3
(B) 3
(C) -4
(D) 4
(E) -5
Rationale: (1) x = 9y+4
(2) 2x = 14y+1
(2)-(1): x=5y-3
5y-x=3
The answer is B.
Answer: (B) 3
Question: In what time will a train 140 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 3.5
(C) 4
(D) 5
(E) 6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 140/40 = 3.5 sec.
Answer: Option B
Answer: (B) 3.5
Question: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?
(A) 14
(B) 16
(C) 17
(D) 20
(E) 26
Rationale: y = product of all elements in set X. now, y will be even if 2 is part of this set (k=2), else y will be odd.
since we have, 11y as an even integer. therefore y must be even. (because 11 is odd, therefore the only way in which 11y can be even is when y is even.)
thus elements in the set X are {2,3,11,7,17,19} and thus its range is 19-2=17;
ANSWER:C
Answer: (C) 17
Question: Calculate the circumference of a circular field whose radius is 12 centimeters.
(A) 2
(B) 4
(C) 26
(D) 24
(E) 10
Rationale: Circumference C is given by
C = 2Ï€r = 2Ï€*12 = 24 Ï€ cm
correct answer D
Answer: (D) 24
Question: The sum of two consecutive numbers is 452. The greatest among these three number is:
(A) 226
(B) 228
(C) 229
(D) 230
(E) 200
Rationale: Let the numbers be x, x + 1
Then,
x + (x + 1) = 452
2x = 450
x = 225
Greatest number, (x + 1) = 226
ANSWER:A
Answer: (A) 226
Question: A certain number when divided by 45 leaves a remainder 31, what is the remainder if the same number be divided by 15?
(A) 13
(B) 11
(C) 9
(D) 1
(E) 3
Rationale: 45 + 31 = 76/15 = 1 (Remainder)
ANSWER:D
Answer: (D) 1
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) 282
(B) 3120
(C) 8383
(D) 8383
(E) 3284
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: (B) 3120
Question: When 25 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
(A) 60
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: Explanation:
Let the number be x. Then,
x - 25 = 7x/12 => x - 7x/12 = 25
5x/12 = 25 => x = 60
Answer: Option E
Answer: (E) 50
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 5 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?
(A) 25
(B) 66
(C) 77
(D) 99
(E) 30
Rationale: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 5(x) = 961
96 + 225 + 490 + 6x = 961
5x = 150 => x = 30.
Answer: E
Answer: (E) 30
Question: A cyclist bikes x distance at 20 miles per hour and returns over the same path at 16 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
(A) 17.6
(B) 17.3
(C) 8.6
(D) 17.2
(E) 9.0
Rationale: Distance = d1 = x miles
Speed = s1 = 20 miles per hour
Time = t1 = Distance/ Speed = x/20
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 16 miles per hour
Time = t2 = Distance/ Speed = x/16
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/20 + x/16 = 9x/80
Speed = 2x/(9x/80) = 160/9
= 17.6
Answer : A
Answer: (A) 17.6
Question: A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 4 kilometers per hour. It returns by the same route at an average speed of 7 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?
(A) 5.1
(B) 7.1
(C) 7.2
(D) 7.5
(E) 8.0
Rationale: Pick a number which is LCM of 7 and 4 = 18.
Upstream time = 28/4 = 7 hrs
Downstream time = 28/7 = 4 hrs
Total time = 11hrs
Total distance = 56
Average Speed = 56/11 = 5.1 km/hr
Answer: (A) 5.1
Question: A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) $40
(B) $60
(C) $80
(D) $90
(E) $100
Rationale: Purchase price = 150
Selling price = x
150 + 0.4*x = x
0.6*x = 150
x = 250
Profit = 250 - 150 = 100
ANSWER:E
Answer: (E) $100
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 9927
(C) 267
(D) 1268
(E) 181
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: (A) 230
Question: If the productivity of a brigade grows by 20% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?
(A) 0.21
(B) 0.82
(C) 1.31
(D) 1.21
(E) 1.44
Rationale: B = 10-men brigade
p = increase in the productivity = 20%
Solution: B x p = B x 1.2 = 1.2B -------> the productivity of 11 men brigade
1.2B x p = 1.2B x 1.1 = 1.31B -----> the productivity of 12 men brigade
The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.31B/B = 1.31
C
Answer: (C) 1.31
Question: There are 8 digit mobile no's. From that how many 8 digit mobile no.'s can be formed if any digit can be repeated and 0 can also start the mobile number?
(A) 9^8
(B) 8^2
(C) 10^8
(D) 9^3
(E) 7^5
Rationale: Here the digits(0,1,2,3,4,5,6,7,8,9) can be repeated and 0 can also be used to start the mobile number. Hence, any of the 10 digits can be placed at each place of the 8 digit number.
10 10 10 10 10 10 10 10
Hence, required number of 8 digit mobile numbers
=10^8
C
Answer: (C) 10^8
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 20 metres apart, how many poles will be needed ?
(A) 55
(B) 56
(C) 14
(D) 58
(E) None of these
Rationale: Solution
Perimeter of the plot = 2(90 + 50) = 280 m.
∴ Number of poles = [280/20] =14m Answer C
Answer: (C) 14
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 80 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 71.5
(B) 72
(C) 72.5
(D) 73
(E) 76.6
Rationale: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 80 kilometers per hour is 1/80 hours = 3,600/80 seconds = 45 seconds;
Time to cover this distance at regular speed is 45+2=47 seconds = 47/3,600 hours = 5/383 hours;
So, we get that to cover 1 kilometer 1/(5/383) hours is needed --> regular speed 76.6 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: E
Answer: (E) 76.6
Question: If logx(3) = 1/4, then x = ?
(A) 61
(B) 71
(C) 81
(D) 91
(E) 101
Rationale: Rewrite the given equation in exponential form
logx(3) = 1/4 if and only if x(1/4) = 3
We now solve, for x, the exponential equation obtained above by raising both sides to the power 4.
(x(1/4)) 4 = 3 4
x = 3 4 = 81
correct answer C
Answer: (C) 81
Question: Find the greatest number that will divide 150, 230 and 175 leaving 50, 5 and 25 as remainders respectively
(A) 19
(B) 17
(C) 32
(D) 9
(E) 8
Rationale: Explanation:
Answer will be HCF of (150-50, 230-5, 175-25)
HCF of (100, 225, 150) = 32
Option C
Answer: (C) 32
Question: In a certain neighborhood , 60 percent of the student are going to school (A) , and the rest are going to school (B) . A new school (C) is opened , If 30 percent of student of school (A) and 40 percent of student of school (B) are expected to go to the new school (C) , what percent of student are expected to go to the new school (C) ?
(A)  30%
(B)  34%
(C)  38%
(D)  42%
(E)  46%
Rationale: Say there are total of 100 students in the neighborhood , 60 students are going to school (A) and 40 student are going to school (B)
60*0.3=18 student of school (A) are expected to go to the new school (C)
40*0.4=16 student of school (B) are expected to go to the new school (C)
Thus total of 18+16=34 student are expected to go to the new school (C) , which is 34% of students .
Answer: B.
Answer: (B)  34%
Question: When 1/20% of 8,000 is subtracted from 1/10 of 8,000, the difference is
(A) 50
(B) 200
(C) 380
(D) 798
(E) 400
Rationale: 1/20 % of 8000 = 4
1/10 of 8000 = 800
800-2 = 798
Ans:D
Answer: (D) 798
Question: A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?
(A) 177 m
(B) 189 m
(C) 160 m
(D) 178 m
(E) 188 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 8
= 160 m.
Answer: C
Answer: (C) 160 m
Question: The speed of a boat in still water in 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 24 minutes is:
(A) 10.6
(B) 10.2
(C) 10.8
(D) 10.4
(E) 10.0
Rationale: Speed downstream = (20 + 5) = 25 kmph
Time = 24 minutes =24/60 hour = 2/5 hour
Distance travelled = Time × speed =2/5×25 = 10.0 km
Answer is E.
Answer: (E) 10.0
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 6%
(C) 4 1/2%
(D) 3 1/2 %
(E) 5 1/2 %
Rationale: Explanation:
160 = (180*4*R)/100
R = 5%
ANSWER IS A
Answer: (A) 5%