mathewhe/aqua_rat huggingface dataset:
Question: in a rectangle 8 vertical and 4 horizontal lines are drawn find the number of rectangle formed
(A) 674
(B) 675
(C) 676
(D) 677
(E) 679
Rationale: 8 vertical lines plus the 2 lines of the existing rectangle(as its mentioned in the question "in a rectangle") accordingly 4 plus 2 horizontal lines.
therefore
10C2*6C2= 675 and if its asked for the new rectangle formed than
675-1=674
ANSWER:A
Answer: (A) 674
Question: A fisherman has 18 fish, then he catches 3 more fish. Now how many fish does he have?
(A) A)21
(B) B)15
(C) C)17
(D) D)23
(E) E)4
Rationale: 18+3=21. Answer is A
Answer: (A) A)21
Question: Find the next number in the Sequence
6, 10, 22, 42, ?
(A) 76
(B) 70
(C) 67
(D) 74
(E) 72
Rationale: +4 =>10
+12 =>22
+20 =>42
+28 =>70
Answer is B
Answer: (B) 70
Question: The length of a rectangular garden is three times its width. If the area of the rectangular garden is 768 square meters, then what is the width of the rectangular garden?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Let x be the width of the garden.
3x^2 = 768
x^2 = 256
x = 16
The answer is A.
Answer: (A) 16
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 26 years
(C) 88 years
(D) 66 years
(E) 12 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: (A) 20 years
Question: Two trains travelling in the same direction at 40 kmph and 22 kmph completely pass each other in 1 minutes. If the length of first train is 125 m, what is the length of second train ?
(A) 125 m
(B) 150m
(C) 175 m
(D) 200m
(E) none of these
Rationale: Let the length of the second train be X.
Speed of both the trains = (40 - 22) x 5/18 = 5 m/s
Thus, (125 + X)/5 = 60 sec
or, 125 + X = 300
or, X = 175m
ANSWER:C
Answer: (C) 175 m
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) Rs.129
(B) Rs.120
(C) Rs.189
(D) Rs.178
(E) Rs.126
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36)
= Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer:C
Answer: (C) Rs.189
Question: AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 16.0 grams
4:00 P.M. x grams
7:00 P.M. 20.4 grams
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
(A) 12.0
(B) 18.1
(C) 12.2
(D) 12.3
(E) 18.0
Rationale: The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.
Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:
Fractional increase from 1 PM to 4 PM = X / 16.0
Fractional increase from 4 PM to 7 PM = 20.4 / X
X \ 16 = 20.4 \ X
X^2 = 20.4 * 16
X = 18
answer : E
Answer: (E) 18.0
Question: What is the place value of 7 in the numeral 51468?
(A) 100
(B) 10
(C) 1
(D) 1000
(E) 11
Rationale: place value of 1 = 1 * 1000 = 1000
Answer is D
Answer: (D) 1000
Question: There are three foam generators in the factory, each of the first two can generate 14 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
(A) 120.
(B) 132.
(C) 146.
(D) 154.
(E) 166
Rationale: Let the foam generators capacity be -
A = 14 lit/hr
B = 14 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 46 lit ( 14 + 14 + 18 ) ; since in 1 and 1/2 hr they will generate 46 + 23 => 69 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 14 lit/hr
C = 18 lit/hr
Total foam generation in 2 hour will be 64 litres {2 (14+18)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 14 => 21 litres
So, total foam generated will be 154 Litres ( 69 + 64 + 21 ) ; hence answer will be (D)
Answer: (D) 154.
Question: If A lends Rs.1000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 112.5
(B) 122.5
(C) 132.5
(D) 114.5
(E) 45
Rationale: (1000*1.5*3)/100 => 45
ANSWER:E
Answer: (E) 45
Question: The difference of and its reciprocal is equal to :
(A) 105/302
(B) 305/309
(C) 105/312
(D) 105/304
(E) 105/309
Rationale: Explanation:
Required difference = 19/16 - 16/19 = = 105/304..
Answer: D) 105/304
Answer: (D) 105/304
Question: A and B started a business in partnership. A invested Rs. 40000 for 6 months. A received Rs.6000 as his share out of the total profit of Rs. 9000, What was the amount invested by B for the whole year?
(A) Rs. 8000
(B) Rs. 10000
(C) Rs. 5000
(D) Rs. 6000
(E) None of these
Rationale: Explanation:
Profits of A and B are distributed in the same ratio of their investment and period of investments.
Investment of A/ Investment of B = Profit of A/ Profit of B = 6000/3000
(40000*1/2)/X*1 = 2/1
Therefore, X = B's investment amount = Rs. 10,000
ANSWER IS B
Answer: (B) Rs. 10000
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 297
(B) 269
(C) 240
(D) 258
(E) 298
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer:C
Answer: (C) 240
Question: How many keystrokes are needed to type the numbers from 1 to 800?
(A) 1804
(B) 1978
(C) 2176
(D) 2292
(E) 2456
Rationale: There are 9 one-digit numbers from 1 to 9.
There are 90 two-digit numbers from 10 to 99.
There are 701 three-digit numbers from 100 to 800.
9 + 90(2) + 701(3) = 2292
The answer is D.
Answer: (D) 2292
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 10000 people who applied for the army and 98 were finally selected, what was the value of N?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 10
Rationale: step(1) 4000 accepted.
step(2) another 40%of 40000=1600 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 1600=800
step(4) 50% of 800=400
Step(5) 50% of 400=200...here we are done with total 5 steps
70% of 200=140
and last step of accepting 70% of 140 =98(our target)
total 7 steps required.
Ans D
Answer: (D) 7
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 14 minutes earlier. How far is the office from his house?
(A) 4 2/5 Km
(B) 4 1/7 Km
(C) 3 1/5 Km
(D) 3 1/7 Km
(E) 3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 22/6
= 24/2 * 22/60
= 11 * 2/5
= 22/5 = 4 2/5 Km
A)
Answer: (A) 4 2/5 Km
Question: If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?
(A) 3/4
(B) 11/12
(C) 15/16
(D) 31/32
(E) 63/64
Rationale: The coin is flipped 5 times in a row.
So there are 2*2*2*2*2 = 32 different outcomes possible such as HHTHH, HTHHT, TTHTH etc
Look for the reverse probability - when will there is no heads or no tails?
There will be no heads when you get all tails. There is only 1 such case TTTTT
There will be no tails when you get all heads. There is again only 1 such case HHHHH
So, out of 32, there are only 2 cases in which there are either no heads or no tails. In all other 30 cases, there is at least one heads and at least one tails.
Required probability = 30/32 = 15/16
Answer (C)
Answer: (C) 15/16
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 5:3
(C) 4:9
(D) 4:4
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš25 : âˆš9 = 5:3.Answer: B
Answer: (B) 5:3
Question: A goods train runs at the speed of 72 kmph and crosses a 260 m long platform in 26 seconds. What is the length of the goods train?
(A) 260 m
(B) 270m
(C) 643m
(D) 832m
(E) 270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 260/26	= 20
x + 260 = 520
x = 260.
Answer:A
Answer: (A) 260 m
Question: 10, 1000, 100000, 10000000....
(A) 100,000,000
(B) 1,000,000,000
(C) 1,000,000,000,000
(D) 100
(E) 1,000,000
Rationale: Each number in this sequence is multiplied by 100. With multiples of ten, it is easiest to remember that you can just transfer all the zeroes on the end of the end of any number. Example: 10 x 100 = 1,000.
Add two digits to the end of 10,000,000 and you get 1,000,000,000.
Answer is B
Answer: (B) 1,000,000,000
Question: In a 400 m race,A covers the distance in 60 seconds and B in 100 second.In this race A beats B by :
(A) 20 m
(B) 125 m
(C) 120 m
(D) 160 m
(E) None of these
Rationale: Solution
Distance covered by B in 40 sec. = (400/100x40)m =160m.
∴ A beats B by 160 metres.
Answer D
Answer: (D) 160 m
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 64 student reduced from 82 to 62 . Due to this the average came down by 16 marks. What was the number of students who took the exam?
(A) 100
(B) 80
(C) 90
(D) 60
(E) 160
Rationale: Explanation :
Number of student = (82-62) * 64/16 = 80
Answer : B
Answer: (B) 80
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 3:5
(B) 5:5
(C) 2:5
(D) 1:6
(E) 2:6
Rationale: C
2:5
Let C.P. = $ 5x and S.P. = $ 7x.
Then, Gain = $ 2x
Required ratio = 2x : 5x = 2:5
Answer: (C) 2:5
Question: In a square , all the mid points are joined. the inner square is shaded. If the area of the square is A, what is the shaded area?
(A) A
(B) A/2
(C) A/3
(D) A/4
(E) A/5
Rationale: the shaded area is half the area of the square (having are A)
therefore answer is A/2
ANSWER:B
Answer: (B) A/2
Question: If 6 (A's capital) = 8 (B's capital) = 8 (C's capital). Then the ratio of their capitals is?
(A) 4:15:16
(B) 4:15:68
(C) 4:3:3
(D) 20:15:11
(E) 20:15:19
Rationale: 6A = 8B = 8 C
A:B:C = 1/6:1/8:1/8
= 4:3:3
Answer: C
Answer: (C) 4:3:3
Question: In bag C there are 5 books and 2 copybooks, in bag D there are 3 books and 3 copybooks. A bag is randomly picked, what is the probability of picking up a book out of bag C?
(A) 2/5.
(B) 5/14.
(C) 3/10.
(D) 3/4
(E) 2/3.
Rationale: Probability of picking up one bagout of two= 1/2
probability of picking 1 book from bag C= 5/7
Hence the desired probability= 1/2*5/7= 5/14
B is the answer
Answer: (B) 5/14.
Question: One fourth of a solution that was 14% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
(A) 24%
(B) 34%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: consider total solution to be 100 liters and in this case you'll have: 75*0.14+25*x=100*0.16 --> x=0.22.
Answer: C.
Answer: (C) 22%
Question: In order to obtain an income of Rs. 450 from 10% stock at Rs. 108, one must make an investment of
(A) 5363
(B) 6240
(C) 4860
(D) 1987
(E) 2732
Rationale: To obtain Rs. 10, investment
= Rs. 108.
To obtain Rs. 450, investment =
= Rs. 4860.
Answer: C
Answer: (C) 4860
Question: Find the value of (28 + 48/69) × 69
(A) 1980
(B) 1982
(C) 1930
(D) 1988
(E) 1680
Rationale: =(28 + 48/69) × 69
=(1932+ 48)/69× 69
=1980/69× 69
=1980
Answer is A.
Answer: (A) 1980
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 30 other employees of Company K, how many employees does Company K have?
(A)  160
(B)  120
(C)  190
(D)  200
(E)  400
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 30
so 25% of x = 30
x = 120
Therefore there a total of 120 employees in the company K
Correct answer - B
Answer: (B)  120
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = P
Set II = {6, 6, 6, 14, 14, 14}, standard deviation = Q
Set III = {10, 10, 10, 10, 10, 10}, standard deviation = R
Rank these three standard deviations from least to greatest.
(A) P, Q, R
(B) P, R, Q
(C) Q, P, R
(D) Q, R, P
(E) R, P, Q
Rationale: SD is minimum when the terms are closer to the mean.
In set 3, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 1 and Set 2, Set 1 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest.
So, Answer is E
Answer: (E) R, P, Q
Question: In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ?
(A) 62
(B) 45
(C) 28
(D) 20
(E) 25
Rationale: Explanation:
Total runs scored = (36 x 5) = 180.
Let the runs scored by E be x.
Then, runs scored by D = x + 5; runs scored by A = x + 8;
runs scored by B = x + x + 5 = 2x + 5;
runs scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x.
So, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120.
Therefore 3x + 120 =180 3X = 60 x = 20.
Answer: Option D
Answer: (D) 20
Question: Of the three-digit integers greater than 660, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 47
(B) 60
(C) 92
(D) 95
(E) 96
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. all three digits are alike;
C. two digits are alike and third digit is different.
We need to calculate C. C = Total - A - B
Total numbers from 660 to 999 = 339 (3-digit numbers greater than 660);
A. all digits are distinct = 3*8+3*9*8 = 240. If first digit is 6 then second digit can take only 3 values (7, 8, or 9) and third digit can take 8 values. If first digit is 7, 8, or 9 (3 values) then second and third digits can take 9 and 8 values respectively;
B. all three digits are alike = 4 (666, 777, 888, 999).
So, 339-240-4=95.
Answer: D
Answer: (D) 95
Question: If n = 30! + 29, then n is divisible by which of the following?
I. 25
II. 27
III. 29
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: 29 divides 30! so 29 also divides 30! + 29.
25 and 27 divide 30! so they do not divide 30! + 29.
The answer is C.
Answer: (C) III only
Question: A man can row with a speed of 12 kmph in still water. If the stream flows at 7 kmph, then the speed in downstream is?
(A) 27
(B) 19
(C) 20
(D) 28
(E) 12
Rationale: M = 12
S = 7
DS = 12 + 7 = 19
Answer: B
Answer: (B) 19
Question: The distance between two planets is 3.08 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
(A)  9.3 × 10^5
(B)  9.9 × 10^6
(C)  9.4 × 10^5
(D)  9.9 × 10^7
(E)  10.1 × 10^8
Rationale: 3.08*10^6 light years = 3.08*10^6/3.26 parsecs.
3.08/3.26 is a little bit less than 1, something like 0.9, thus 3.08*10^6/3.26 = ~0.94*10^6 = 9.4*10^5.
Answer: C.
Answer: (C)  9.4 × 10^5
Question: A student traveled 10 percent of the distance of the trip alone, continued another 30 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?
(A) 75
(B) 100
(C) 125
(D) 150
(E) 175
Rationale: Let x be the total length of the trip.
0.1x + 30 miles + 0.5x = x
30 miles = 0.4x
x = 75 miles
The answer is A.
Answer: (A) 75
Question: Walking at 5/6th of its usual speed a cab is 15mnts late. Find its usual time to cover the journey?
(A) 25m
(B) 45m
(C) 32m
(D) 75m
(E) 62m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 15m
UT/5 = 15m
UT = 75m
Answer is D
Answer: (D) 75m
Question: A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
(A) 7 hours
(B) 7 hours 30 min
(C) 7 hours 35 min
(D) 7 hours 45 min
(E) 9 hours 35 min
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time
which will be a real benefit for you.
D
Answer: (D) 7 hours 45 min
Question: A runs 1 ¾ times as fast as B. if A gives B a start of 84 m, bow far must winning post be so that A and B might reach it at the same time?
(A) 85 m
(B) 98 m
(C) 196 m
(D) 123 m
(E) 213 m
Rationale: Ratio of the rates of A and B = 7/4 : 1 = 7 : 4.
So, in a race of 7 m, A gains 3m over B.
:. 3 m are gained by A in a race of 7 m.
:. 84 m are gained by A in a race of (7/3 x 84) m = 196 m.
:. Winning post must be 196 m away from the starting point.
ANSWER C 196 m
Answer: (C) 196 m
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 98
(B) 179
(C) 268
(D) 102
(E) 105
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: E
Answer: (E) 105
Question: I. q-14, q, q, q, q+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?
(A) I, II, III
(B) I, III, II
(C) II, III, I
(D) III, I, II
(E) III, II, I
Rationale: S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of q or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.
A.
Answer: (A) I, II, III
Question: 10,995,1839,91635, 279570 which number is wrong in series
(A) 10
(B) 27950
(C) 995
(D) 1839
(E) 91635
Rationale: 1839...........
all are multiples of 5 expect 1839
ANSWER:D
Answer: (D) 1839
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 4 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage lesser than the typical dosage?
(A) 8%
(B) 9%
(C) 11%
(D) 12.5%
(E) -87.5%
Rationale: Typical dosage per 15 pound of the body weight = 4 c.c
Typical dosage per 120 pound of the body weight = 4 *(120/15)
= 4 * 8
= 32 c.c
Dosage prescribed by doctor for 120 pound patient = 18 c.c
% prescribed dosage greater than the typical dosage = (18-32/16) *100%
=(-14/16) *100%
= -87..5%
Answer E
Answer: (E) -87.5%
Question: Find the 25% of Rs. 300.
(A) s. 50
(B) s. 70
(C) s. 100
(D) s. 80
(E) s. 75
Rationale: Explanation :
25% of 300
=> 25/100 *300 = Rs. 75
Answer : E
Answer: (E) s. 75
Question: Find the smallest number of five digits exactly divisible by 32,40,56 and 64.
(A) 11020
(B) 11030
(C) 11040
(D) 11060
(E) 11080
Rationale: Smallest number of five digits is 10000.
Required number must be divisible by L.C.M. of 32,40,56,64 i.e 2240,
On dividing 10000 by 2240,we get 1200 as remainder.
Therefore, Required number = 10000 +( 2240 â€“ 1200 ) = 11040.
Answer is C.
Answer: (C) 11040
Question: Let x be a positive integer, what is the remainder when 5^(3x+1)+5 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: For: (5^(3x+1)+5)/3
Let n = 3x + 1
5^n
5^1 = 5
5^2 = 25
5^3 = 125, ... last digit is always 5.
Rule: x^(m+n) = (x^m)(x^n)
(5^(3x))(5^1)
Rule: x^(mn) = (x^m)^n
((5^3)^x)(5) => Now, (5)(125^x) + 5 = (5)(5) + 5 => Finally, 30/5 divides evenly with 0 remainder.
Answer: A
Answer: (A) 0
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -4
III. 2
IV. 5
(A) I and II only
(B) I and III only
(C) II and III only
(D) II and IV only
(E) I, II, III,
Rationale: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 2 and 3 satisfy both inequalities.
Answer: D.
Answer: (D) II and IV only
Question: A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 15 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 22
(E) 40
Rationale: I treat such problems as work ones.
Work=Rate*Time
Mileage(m)=Rate(mpg)*Gallons(g)
X gallons is a full tank
{462=RX
{336=(R-15)X solve for R, R=55
55-15=40 mpg
E
Answer: (E) 40
Question: Anintegratedteam consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 7 members and the design team has 3 members, how manyintegratedteam formations are possible?
(A)  36
(B)  54
(C)  63
(D)  90
(E)  112
Rationale: 2 out of 7 times 2 out of 3 => 7*6/2*1 * 3*2/2*1 = 63
C
Answer: (C)  63
Question: A box contains seven bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
(A) 2045/2401
(B) 2121/2401
(C) 2145/2401
(D) 2345/2401
(E) 2245/2401
Rationale: Required probability
= 1 - 256/2401
= 2145/2401
Answer: C
Answer: (C) 2145/2401
Question: On the shelf, there are four books of poetry, four novels, and five reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?
(A) 4/25
(B) 6/31
(C) 8/35
(D) 10/39
(E) 12/41
Rationale: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.
P(one novel and one reference work) = 4/13*5/12 + 5/13*4/12 = 10/39
The answer is D.
Answer: (D) 10/39
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 48. What is a possible value for the mean of the distribution?
(A) 46
(B) 47
(C) 48
(D) 55
(E) 50
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 48:
{Mean} - 3*{SD} > 48;
{Mean} - 6 > 48;
{Mean} > 54.
Answer: D.
Answer: (D) 55
Question: Magnabulk Corp sells boxes holding n magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
(A) 100bn/m
(B) 100m/(bn)
(C) bn/(100m)
(D) m/(bn)
(E) bn/m
Rationale: crate has = bn magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = 100 m / bn
Ans; B
Answer: (B) 100m/(bn)
Question: What is the length of a bridge (in meters), which a train 148 meters long and travelling at 45 km/h can cross in 30 seconds?
(A) 211
(B) 219
(C) 227
(D) 235
(E) 243
Rationale: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 30 seconds, the train can travel 25/2 * 30 = 375 meters
375 = length of train + length of bridge
length of bridge = 375 - 148 = 227 meters
The answer is C.
Answer: (C) 227