mathewhe/aqua_rat huggingface dataset:
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 18) both lie on the line defined by the equation x = (y/6) - (2/5), what is the value of p?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x = (y/6) - (2/5), and so y = 6x + 12/5. The slope is 6.
(n+18-n) / (m+p-m) = 6
p = 3
The answer is C.
Answer: (C) 3
Question: Three candidates contested an election and received 500, 7632 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 60%
(C) 58.8%
(D) 90%
(E) 80%
Rationale: total votes are 19760 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11628/19760 = 58.8%
ANSWER:C
Answer: (C) 58.8%
Question: There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total T of the book?
(A) 3003
(B) 3027
(C) 3024
(D) 3021
(E) 3018
Rationale: First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)T
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: (A) 3003
Question: Ben likes long bike rides. On one ride, he goes biking for six hours. For the rst hour, he bikes
at a speed of 15 miles per hour. For the next two hours, he bikes at a speed of 12 miles per
hour. He remembers biking 90 miles over the six hours. Compute the average speed, in miles
per hour, Ben biked during the last three hours of his trip.
(A) 20
(B) 35
(C) 17
(D) 51
(E) 46
Rationale: Ben biked 90-15- 2 * 12 = 51 miles over the last three hours, averaging a speed of
51/3 = 17 miles per hour.
correct answer C
Answer: (C) 17
Question: The Guests at a football banquet consumed a total of 411 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?
(A) 165
(B) 161
(C) 162
(D) 163
(E) 164
Rationale: To minimize one quantity maximize other.
164*2.5 (max possible amount of food a guest could consume) = 410 pounds, so there must be more than 164 guests, next integer is 165.
Answer: A.
Answer: (A) 165
Question: The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 3 unit of standard deviation above the mean?
(A) -35.6 degrees Celsius
(B) -33.0 degrees Celsius
(C) -30.4 degrees Celsius
(D) -27.8 degrees Celsius
(E) -25.2 degrees Celsius
Rationale: Let us suppose mean = M and SD = d.
So, we are given M - 2d = -38.2
and M + 4d = -22.6
solving both the equations, we will get M = -33 an d = 2.6
So, we need to find out M + 3d = -33 +3* 2.6 = -25.2. Hence, E
Answer: (E) -25.2 degrees Celsius
Question: Find the odd man out. 5, 6, 14, 45, 185, 925, 5556
(A) 5556
(B) 925
(C) 185
(D) 6
(E) None of these
Rationale: Explanation :
5 × 1 + 1 = 6
6 × 2 + 2 = 14
14 × 3 + 3 = 45
45 × 4 + 4 = 184
184 × 5 + 5 = 925
925 × 6 + 6 = 5556
Hence, it is clear that 184 should have come instead of 185. Answer : Option C
Answer: (C) 185
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 15 1/9%
(B) 11 8/9%
(C) 11 1/9%
(D) 16 1/9%
(E) 11 1/2%
Rationale: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer:C
Answer: (C) 11 1/9%
Question: What is the principal sum?
I. The sum amounts to Rs. 720 in 4 years at S.I.
II. The sum amounts to Rs. 810 in 7 years at S.I.
III. The rate of interest is 10% p.a.
(A) I and III only
(B) II and III only
(C) I and II only
(D) Any one of the three
(E) Any two of the above
Rationale: Explanation:
Clearly, any of the three will give us the answer
Answer: E
Answer: (E) Any two of the above
Question: Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/10 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
(A) 21
(B) 35
(C) 39
(D) 30
(E) 65
Rationale: The total number of the people in the room must be a multiple of both 7 and 10 (in order 3/7 and 5/10 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 10, which is 70.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.
Therefore there are 3/7*70=30 people in the room under the age of 21.
Answer: D.
Answer: (D) 30
Question: What is 121 times 11?
(A) 1331
(B) 1313
(C) 1133
(D) 3131
(E) 3311
Rationale: A 1331
Answer: (A) 1331
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
(A) 5729
(B) 5760
(C) 7200
(D) 2870
(E) 2799
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 5= 7200.Answer: C
Answer: (C) 7200
Question: 44Ã—98Ã—101=?
(A) 435512
(B) 434431
(C) 548654
(D) 543286
(E) 546543
Rationale: 44Ã—(100-2)Ã—(100+1)
(4400-88)Ã—(100+1)
4312Ã—(100+1)
431200+4312=435512
answer A
Answer: (A) 435512
Question: A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5 km on foot. His total journey is :
(A) 125 km
(B) 130 km
(C) 135 km
(D) 140 km
(E) None
Rationale: Sol.
Let the total journey be x km. Then
3x/5 + 7x/20 + 6.5 = x
⇔ 12x + 7x + 20 * 6.5 = 20x
⇔ x = 130 km.
Answer B
Answer: (B) 130 km
Question: If k^3 is divisible by 120, what is the least possible value of integer k?
(A) 15
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: k^3 = 120*x = 2^3*3*5*x
The factors of k must at minimum include 2*3*5 = 30.
The answer is B.
Answer: (B) 30
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?
(A) 3
(B) 14
(C) 30
(D) 42
(E) 70
Rationale: Let's try the Prime Box Approach
Prime Box is simply a collection of all prime factors of a given number!
(1) Prime Box of 16 = |2, 2, 2, 2|
(2) Prime Box of 45 = |3, 3, 5|
(3) Prime Box of n = |2, 2, 3....|
(4) Prime Box of 210 = |2, 5, 3, 7|
From 3 and 4:
The GCF of n and 210 must be a multiple of 6.
So we can eliminate A, B and E!
From 2 and 3:
n is not a multiple of 5. If it were, the GCF of n and 45 would have been 15!
So we can eliminate C
The only remaining choice is 'D'
Answer: (D) 42
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 477
(B) 432
(C) 279
(D) 276
(E) 291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 15 + 21 = 36
T = 12
D = 36 * 12 = 432.Answer: B
Answer: (B) 432
Question: Solomon taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?
(A) A)165
(B) B)220
(C) C)310
(D) D)185
(E) E)181
Rationale: Loan amount : Rs.15000/- @ 11.5%
Interest per month = 15000/- * 11.5% =Rs.1725
Interest for one day = 1725/30=57.50
Interest for 7 days is = 57.50*7 =403
FD amount is = Rs.10000/- @ 9.5%
Interest per month = 10000 * 9.5% = 950/-
Interest for 7 days = 950/30*7 = 222
Interest amount to be paid by Solomon = 403-222 =181/- for 7 days
Answer is E
Answer: (E) E)181
Question: Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 3, 4, 5, 6, and 7 seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 1:00 pm (i.e. one hour later)?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: The least common multiple is 2*2*3*5*7=420.
3600 seconds / 420 = 8 + remainder.
The answer is B.
Answer: (B) 8
Question: A number is divided by 406 leaves remainder 115,what will be the remainder when it will be divided by 29?
(A) 26
(B) 30
(C) 27
(D) 28
(E) 29
Rationale: Let the Number be N.
So N=406x+115.
Now divide this number by 29
As 406 is exactly divisible by 29,we have to divide 115 by 29 and find the remainder.
So Remainder is 28
Option D is answer
Answer: (D) 28
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 2288
(B) 277
(C) 9888
(D) 5460
(E) 2777
Rationale: 5000 * 104/100 * 105/100 => 5460,Answer: C
Answer: (C) 9888
Question: A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 75 km/hr. What is the speed of the car in the second half of the trip?
(A) 40
(B) 45
(C) 48
(D) 50
(E) 55
Rationale: Let D be the distance and let V be the speed in the second half.
The total time = T1 + T2
D/60 = D/150 + (D/2) / V
D/100 = D/2V and so V = 50 km/hr
The answer is D.
Answer: (D) 50
Question: There is one four-digit whole number n, such that the last four digits of n2 are in fact the original number n
(A) 8476
(B) 7376
(C) 9376
(D) 7378
(E) 9466
Rationale: C
9376
Looking at the last digit, the last digit must be either 0, 1, 5 or 6.
Then looking at the last two digits, the last two digits must be either 00, 01, 25 or 76.
Then looking at the last three digits, the last three digits must be either 000, 001, 625 or 376.
Then looking at the last four digits, the last four digits must be either 0000, 0001, 0625 or 9376.
Out of those, only 9376 is a 4 digit number
Answer: (C) 9376
Question: A train 600 m long can cross an over brdge of 100m long in 70 sec and then find the speed of the train?
(A) 79
(B) 30
(C) 36
(D) 66
(E) 12
Rationale: Length = Speed * time
Speed = L/T
S = 700/70
S = 10 M/Sec
Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 36Kmph.Answer:C
Answer: (C) 36
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5830, what is the length of the plot in metres?
(A) 333
(B) 200
(C) 288
(D) 276
(E) 220
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 5830
[4L - 40] = 5830 / 26.50 = 220
4L = 260
L = 260/4= 65 meters.
Answer: E
Answer: (E) 220
Question: A man engaged a servant on a condition that he'll pay Rs 90 and also give him a bag at the end of the yr. He served for 9 months and was given a turban and Rs 65. So the price of turban is
(A) Rs 10
(B) Rs 9
(C) Rs 0
(D) Rs 55
(E) Rs 8
Rationale: Let the value of turban =Rs x
For 1 year=90+x
For 9 months(i,e 3/4 year)=65+x
i,e
1:(90+x)::3/4:(65+x)
i,e
(90+x)/(65+x)=1/(3/4)
270+3x=260+4x
Thus x=10
ANSWER:A
Answer: (A) Rs 10
Question: A train covers a distance of 100km in 1 hour. If its speed is decreased by 15km/hr, the time taken by the car to cover the same distance will be?
(A) 1hr
(B) 1hr 10min
(C) 50min
(D) 1hr 30min
(E) 1hr 45min
Rationale: Speed = 100/1 = 100km/hr
New speed = 100-15= 85 km/hr
Time taken = 100/85 = 1hr 10min
Answer is B
Answer: (B) 1hr 10min
Question: Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 55-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs?
(A) 15
(B) 28
(C) 18
(D) 24
(E) 21
Rationale: let x be the number of 55 ounce cans. Therefore (x+30) is the number of 15 ounce cans.
Total volume is same, therefore
55x=15(x+30)
30x=450
x=15
Ans - A
Answer: (A) 15
Question: Find the value of (1/(2*3))+(1/(3*4))+(1/(4*5))+(1/(5*6))+…..+ ((1/(9*10)).
(A) 2/5
(B) 1/5
(C) 4/5
(D) 3/5
(E) None of them
Rationale: Given expression=((1/2)-(1/3))+((1/3)-(1/4))+((1/4)-(1/5))+
((1/5)-(1/6))+….+ ((1/9)-(1/10))
=((1/2)-(1/10))=4/10 = 2/5.
Answer is A.
Answer: (A) 2/5
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 85, what is the value of K?
(A)  11
(B)  15 3/4
(C)  31
(D)  23
(E)  25 3/10
Rationale: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 85
11K = 85 * 4 +1 = 340 +1 = 341
K = 253 / 11 = 31.
Answer C.
Answer: (C)  31
Question: If (1+f)g=g, which of the following must be true?
(A) f=-1 or g=0
(B) f=0 or g=0
(C) f=1 or g=1
(D) f=-1 or g=-1
(E) f=0 or g=1
Rationale: By only having fg=0, we cannot say answer is B as A and E options also satisfy the condition fg=0. ans B
Answer: (B) f=0 or g=0
Question: The area of a rhombus is equal to the area of a square whose side length is 8cm. If one of the diagonals is 16cm what is the length of other diagonal?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 20
Rationale: Area of the square=8x8=64
Let 'l' be the unknown diagonal
0.5 x 16 x 'l' = 64 which gives 'l'=8cm
Answer: B
Answer: (B) 8
Question: If p and q are integers, such that p < 6 < q, and s is a nonnegative integer, which of the following must be true?
(A) p^2 < q^2
(B) p + q = 0
(C) sp < sq
(D) sp ≠ sq
(E) p/q < s
Rationale: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.
P = -2
Q = 1
S = 0
Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE
Answer B: P+Q=0... -2+1 = -1 NOT TRUE
Answer C: SP < SQ... 0 < 0 is TRUE
Answer D: SP ≠ SQ... 0 = 0 NOT TRUE
Answer E: P/Q < S... -2/1 < 0 not TRUE
C
Answer: (C) sp < sq
Question: Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 50 yr. How old is E?
(A) 50 yr
(B) 40 yr
(C) 45yr
(D) 64 yr
(E) NOne
Rationale: Solution:
Total present age of A, B, C and D,
= (45*4)+(4*5) = 200 yr;
Total age present age of A, B, C, D and E,
= 50*5 = 250 yr.
So, age of E = 50 yr.
Answer: Option A
Answer: (A) 50 yr
Question: What is the average of 1/2, 2/5 and 7/10?
(A) 1/5
(B) 3/10
(C) 8/15
(D) 1/2
(E) 6/5
Rationale: Sum of 1/2,2/5,7/10 =16/10
Average = 16/10*1/3 =8/15
Answer C 8/15
Answer: (C) 8/15
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
(A) 45
(B) 23
(C) 38
(D) 27
(E) 28
Rationale: Explanation:
A:B:C = (10×7):(12×5):(15×3)
= 70 :60 :45
= 14 :12 :9
C's rent = Rs.(175×9/35)
=Rs. 45.
Answer: A) Rs. 45
Answer: (A) 45
Question: When a certain number X is divided by 143, the remainder is 59 Which of the following numbers, if added to X, would result in a number divisible by 13?
(A) 7
(B) 21
(C) 34
(D) 47
(E) 6
Rationale: Now X= 143q + 58 = 11*13*q + 58..so we have to make only 58 div by 13..
59 + 6 = 65 divisible by 13 ..add 6
ans E
Answer: (E) 6
Question: What is the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers?
(A) 7, 4
(B) 8, 6
(C) 6, 4
(D) 3, 2
(E) None of these
Rationale: Sol. (c) A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
i.e., 58N is divisible by 8.
Clearly,N = 4
Again, a number is divisible by 11 if the difference between the sum of digits at even places and sum of digits at the odd places is either 0 or is divisible by 11.
i.e (M + 9 + 4 + 4 + 8) - (3 + 0 + 8 + 5 + N)
= M + 25 - (16 + N)
= M - N + 9 must be zero or it must be divisible by 11.
i.e M - N = 2
=> M = 2 + 4 = 6
Hence, M = 6 , N = 4
Answer C
Answer: (C) 6, 4
Question: In a division sum, the quotient is 18, the divisor 43 and the remainder 12, find the dividend?
(A) 586
(B) 766
(C) 796
(D) 786
(E) 686
Rationale: Explanation:
18 * 43 + 12 = 786
Answer : D
Answer: (D) 786
Question: Your new cell phone battery needs to be charged for 3 hours and 45 minutes before
using it. If you plug the battery into the charger at 8:20 a.m., you should wait till what
time before using it?
(A) 09:05 a.m.
(B) 11:05 a.m.
(C) 12:05 p.m.
(D) 13:05 p.m.
(E) 15:05 p.m.
Rationale: 8:20 + 3 hours = 11:20
+ 0:45 minutes = 12: 05 P.m.
Answer: 12:05 p.m.
correct answer C
Answer: (C) 12:05 p.m.
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 1 kmph
(B) 4 kmph
(C) 9 kmph
(D) 5 kmph
(E) 5 kmph
Rationale: Explanation:
M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: Option B
Answer: (B) 4 kmph
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 35% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
(A) 18%
(B) 20%
(C) 21%
(D) 35%
(E) Cannot be determined
Rationale: Answer: D.
Answer: (D) 35%
Question: There are 6 people in the elevator. Their average weight is 170 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
(A) 37
(B) 168
(C) 189
(D) 190
(E) 200
Rationale: Solution
Average of 7 people after the last one enters = 151 .
âˆ´ Required weight = (7x151)-(6x170)
= 1057- 1020
= 37.
Answer A
Answer: (A) 37
Question: Rs 60000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%?
(A) 30000
(B) 40000
(C) 50000
(D) 60000
(E) 70000
Rationale: let first parrt is x and second part is y then x+y=60000----------eq1
total profit=profit on x +profit on y
7000=(x*10*1)/100 + (y*20*1)/100
70000=x+2y-----------------------------------eq2
70000=60000+y
so y=10000 then x =50000-10000=40000
first part =40000
ANSWER:B
Answer: (B) 40000
Question: An article sold at a profit of 20%. If both the cost price and selling price would be Rs.20/- less, the profit would be increased by 10%. What is the price of that article?
(A) Rs 60
(B) Rs 50
(C) Rs 65
(D) Rs 62
(E) Rs 68
Rationale: Actual price = Rs 60 and selling price with 20% profit = Rs. 72.
If CP and SP is Rs 20 less, then
CP=Rs 40 and SP = Rs 52 and hence, the profit is 30%.
CP = Rs 60.
ANSWER:A
Answer: (A) Rs 60
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 4/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) 7/31
(B) 7/15
(C) 10/21
(D) 17/35
(E) 1/2
Rationale: Let the total # of cups be 10.
# of small cups sold 4/5*10=8;
# of large cups sold 10-8=2;
Let the price of small cup be $6, then the price of larges cup would be 7/6*6=$7;
Revenue from small cups:8*$6=$48
Revenue from large cups cups: 2*$7=$14;
Fraction of total revenue from large cups: 14/(14+48)=7/31.
Answer: A.
Answer: (A) 7/31
Question: The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a raƟo
less than 16 : 21, is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Let x is subtracted.
Then,
(6−x)(7−x)<162121(6�x)<16(7�x)=>5x>14=x>2.8
Least such number is 3
Answer: A
Answer: (A) 3
Question: The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Let 2x be the number of spinsters. Then 7x is the number of cats.
7x-2x=40
x=8 and the number of spinsters is 2(8)=16.
The answer is B.
Answer: (B) 16
Question: The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Bren 10 years from now?
(A) 17
(B) 25
(C) 27
(D) 35
(E) 50
Rationale: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-8 + 8x-8 + 7x-8 = 76
x = 5
Present age of Bren = 8*5 = 40
Bren's age 10 years hence = 40+10 = 50
Answer = E
Answer: (E) 50
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
(A) 30
(B) 35
(C) 40
(D) 47
(E) 50
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Answer: (C) 40
Question: If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 14 days. If he works at reduced efficiency, he can work without break and finish that same job in 14 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?
(A) 3/9
(B) 4/5
(C) 3/2
(D) 4/6
(E) 5/2
Rationale: We're told that there are 2 ways for Dale to complete a job:
1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 14 days.
2) Reduced Efficiency: 14 straight days with no days off.
Working at Full Efficiency creates the following pattern:
2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2+1+2= 14 days
Totals: 10 days on, 4 days off
Reduced Efficiency means that Dale will do 10 days of work in 14 days, thus those Reduceddaysare 10/4=5/2 of Full Efficiency.
Answer : E
Answer: (E) 5/2
Question: Evaluate:7899665 - 12*3*2 =?
(A) 2455835
(B) 2789255
(C) 6868575
(D) 7899657
(E) 1023666
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
7899665 - 12*3*2 = 7899665 - 8 = 7899657
correct answer D
Answer: (D) 7899657
Question: The average salary of 20 workers in an office is Rs.1900 per month. If the manager's salary is added, the average salary becomes Rs.2000 p.m. What is the manager's annual salary?
(A) Rs.24,000
(B) Rs.25,200
(C) Rs.45,600
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Manager's salary per month
= (Rs.21×2000−20×1900)) = Rs.4000
Manager's Annual salary = Rs.(4000×12)=Rs.48000
Correct Option:D
Answer: (D) None of these
Question: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is
(A) 7
(B) 8
(C) 9
(D) 24
(E) 23
Rationale: To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle.
ANSWER:D
Answer: (D) 24
Question: What percentage of numbers from 1 to 50 have squares that end in the digit 4?
(A) 1
(B) 14
(C) 25
(D) 21
(E) None of the these
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 4. Such numbers from 1 to 50 are 2,8,12,18,22,28,32,38,42,48.
Number of such numbers = 10.
Required percentage = (10/50 * 100) = 20%
ANSWER:E
Answer: (E) None of the these
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
(A) Rs. 9400
(B) Rs. 8900
(C) Rs. 8400
(D) Rs. 3400
(E) Rs. 8440
Rationale: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
Answer:C
Answer: (C) Rs. 8400
Question: Two numbers are in the ratio of 5:7. If 7 is subtracted from each number, they are in the ratio of 2:3. What are the two numbers?
(A) 35, 49
(B) 40, 56
(C) 45, 63
(D) 50, 70
(E) 55, 77
Rationale: (5x-7):(7x-7) = 2y:3y
5x - 7 = 2y
7x - 7 = 3y
49-35 = 15y - 14y
14 = y
5x-7 = 28
x = 7
The two numbers are 5x and 7x which are 35 and 49.
The answer is A.
Answer: (A) 35, 49