mathewhe/aqua_rat huggingface dataset:
Question: What is the minimum value of |x-4| + |x+5| + |x-5| ?
(A) -3
(B) 3
(C) 5
(D) 7
(E) 10
Rationale: A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.
|x-4| >= 0 --> Minimum occurs at x = 4
|x+5| >= 0 --> Minimum occurs at x = -5
|x-5| >= 0 --> Minimum occurs at x = 5
x = -5 --> Result = 9 + 0 + 10 = 19. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.
x = 4 --> Result = 0 + 9 + 1 = 10
x = 5 --> Result = 1 + 10 + 0 = 11
So minimum value of the expression occurs at x = 4 and the resultant value = 10
Answer: E
Answer: (E) 10
Question: How many positive integers less than 100 are neither multiples of 2 or5.
(A) a)30
(B) b)31
(C) c)40
(D) d)33
(E) e)34
Rationale: To answer this Q we require to know
1) multiples of 2 till 100 = 100/2 = 50
2) Multiples of 5 till 100 = 100/5 = 20
add the two 50+20=70 ; subtract common terms that are multiple of both 2 and 5..
LCM of 2 and 5 = 10
Multiples of 10 till 100 = 100/10 = 10
so total multiples of 2 and 5 = 70-10 = 6
ans = 100-60 = 40
C
Answer: (C) c)40
Question: Two representatives must be selected from each of two groups of students. One group consists of three men and two woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 5/12
Rationale: Group 1: 3 Men and 2 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*2*1*2 = 12 ways
Total Favorable cases = 3+12 = 15
Total Possible ways of selecting students 2 from each group = 4C2*4C2 = 6*6 = 36
Probability = 15/36 = 5/12
Answer : Option E
Answer: (E) 5/12
Question: Divide Rs.32000 in the ratio 1:7?
(A) 12000, 20000
(B) 12000, 200098
(C) 4000, 28000
(D) 12000, 20006
(E) 12000, 20001
Rationale: 1/8 * 32000 = 4000
7/8 * 32000 = 28000
Answer: C
Answer: (C) 4000, 28000
Question: If the same letters represent the same digit and different letters represent different digits, what digit does the letter A represent?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Look at the digits in the ones place, there are 2 possible values for A + B + B:
A + B + B = A or A + B + B = 10 + A.
If A + B + B = A , B = 0. If A + B + B = 10 + A, B = 5.
Since B is a leading digit of BA, B cannot be a 0. B has to be a 5.
Look at the digits in the tens place, there are 2 possible values for 5 + A + A + 1:
5 + A + A + 1 = 10 + A or 5 + A + A + 1 = 20 + A
If 5 + A + A + 1 = 10 + A, A = 4. If 5 + A + A + 1 = 20 + A, A = 14. Since A is a single digit number, A has to be 4.
correct answer D
Answer: (D) 4
Question: Convert the following in a fraction: 0.75%
(A) 75/100
(B) 3/4
(C) 1/75
(D) 2/5
(E) None of the Above
Rationale: 0.75 =75/100 = 3/4
Answer is B.
Answer: (B) 3/4
Question: A bowl was filled with 100 ounces of milk, and 0.0001 ounce of the milk evaporated each day during a 50-day period. What percent of the original amount of milk evaporated during this period?
(A) A)0.005%
(B) B)0.05%
(C) C)5%
(D) D)50%
(E) E)52%
Rationale: Total amount of milk evaporated each day during a 50-day period = .0001 * 50
= .005
percent of the original amount of milk evaporated during this period = (.005/100) * 100%
= 0.005 %
Answer A
Answer: (A) A)0.005%
Question: Ashley and Vinie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vinie will be chosen?
(A) 1/10
(B) 3/28
(C) 2/9
(D) 1/4
(E) 1/2
Rationale: I did slightly different and hence obviously ended up with the answer 2/9.
I assumed that because Ashley and Vinie have to be chosen, the remaining selection is 3 people from 8.
8C3/10C5= 2/9. Option C.
Answer: (C) 2/9
Question: AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 7 of them still work in AMS is ?
(A) 0.19
(B) 1.22
(C) 0.1
(D) 0.04096
(E) none of these
Rationale: Asking atleast 6 of them continue ,
it has 3 cases.
1 all 8 professors continue.
2 7 professors continue and 1 professors discontinue.
1st case all 8 continue is = 2/10*3/10*4/10*5/10*6/10*7/10*/8/10*9/10=9factorial/10power8
=362880/100000000
=>0.00363.
2nd case any 7 professors continue, and 1out of 8 discontinue ,8C1 means 8 ways.
= 2/10*3/10.......8/10*1/10, (9/10 prodbability professor discontinue then 1/10)
in this way if we calculate for 8 possibilities then value is =>0.03733.
=0.00363+0.03733+0.1436=0.18456=0.04096
D
Answer: (D) 0.04096
Question: Virat buys an old car for Rs. 40000 and spends Rs. 4000 on its repairs. If he sells the car for Rs. 60000, his gain percent is:
(A) 3 (4/7) %
(B) 11 (1/9) %
(C) 12 (2/3) %
(D) 12%
(E) 36.36%
Rationale: Explanation:
C.P. = Rs. (40000 + 4000) = Rs. 44000
S.P. = Rs. 60000.
Gain% = ( (16000 / 44000) * 100 ) % = 36.36%
ANSWER E
Answer: (E) 36.36%
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 50 minutes, how many times do they toll together?
(A) 4
(B) 10
(C) 15
(D) 16
(E) 26
Rationale: L.C.M of 2,4,6,8,10,12 is 120. i.e after each 2 min they will toll together.So in 50 min they will toll 25 times.As they have initially tolled once,The answer will be 25+1=26.
ANSWER:E
Answer: (E) 26
Question: If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is?
(A) 426
(B) 526
(C) 207
(D) 204
(E) 297
Rationale: Given ratio
= 1/2:2/3:3/4 = 6:8:9
1st part = 782 * 6/23
= Rs. 204.
Answer:D
Answer: (D) 204
Question: Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 56, 91
(A) 22
(B) 91
(C) 37
(D) 28
(E) 21
Rationale: Explanation:
1, 1 + 12 = 2, 2 + 22 = 6, 6 + 32 = 15, 15 + 42 = 31, 31 + 52 = 56, 56 + 62 = 92
Last number of given series must be 92 not 91.
Answer: B) 91
Answer: (B) 91
Question: rahul played weel in this season.his current batting averagge is 46.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
(A) 8
(B) 10
(C) 3
(D) 6
(E) 5
Rationale: 46x+78=54(x+1)
=>8x=24
=>x=3
ANSWER:C
Answer: (C) 3
Question: The simple interest on Rs. 34 for 8 months at the rate of 6 paise per rupeeper month is
(A) 16.32
(B) 16.9
(C) 12.25
(D) 13.21
(E) None
Rationale: Sol.
S.I. = Rs. [34 * 6/100 * 8] = Rs. 16.32
Answer A
Answer: (A) 16.32
Question: A train running at the speed of 58 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 145
(B) 272
(C) 278
(D) 277
(E) 112
Rationale: Speed = 58*(5/18) m/sec = 145/9 m/sec
Length of Train (Distance) = Speed * Time
(145/9) * 9
= 145 meter
Answer: A
Answer: (A) 145
Question: Calculate the average mark scored by Andrea if he had the following scores in an examination: 66, 60, 72, 77, 55 and 85 marks (out of 100) in English, Mathematics, Chemistry, Biology, French Language and Physics respectively?
(A) 74
(B) 76
(C) 70
(D) 67
(E) 69.2
Rationale: Explanation:
Average mark = 66+60+72+77+55+85/6=69.2
Answer: Option E
Answer: (E) 69.2
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 70 paise per sq. metre
(A) s595
(B) s780
(C) s880
(D) s480
(E) s980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*70
= 59500p
in Rs =59500/100=Rs595
ANSWER:A
Answer: (A) s595
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average one number, namely 36 was wrongly read as 26. The correct average is :
(A) 12.4
(B) 14
(C) 16
(D) 18.6
(E) None of these
Rationale: Explanation:
Sum of numbers = (10××15-26+36)=160
Correct average = 160/10=16
Correct Option: C
Answer: (C) 16
Question: A woman sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
(A) 11%
(B) 700%
(C) 430%
(D) 9%
(E) 125
Rationale: D
(30*30)/100 = 9%loss
Answer: (D) 9%
Question: A man sells an article at 15% loss. Had he sold it for Rs. 70/- more he could have gained 20%. What is the cost price of the article?
(A) Rs.200/-
(B) Rs.400/-
(C) Rs.460/-
(D) Rs.480/-
(E) None of these
Rationale: Explanation:
Short cut method:
Loss =====> 15 %
Profit ====> 20 %
~
----------------
35 % ---------> Rs. 70/-
100 % --------> Rs. 200/-
Answer: Option A
Answer: (A) Rs.200/-
Question: The sector of a circle has radius of 21 cm and central angle 180o. Find its perimeter?
(A) 91.5
(B) 92
(C) 108
(D) 94
(E) 95
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 108 cm
Answer: Option C
Answer: (C) 108
Question: If 40% of a number exceeds 25% of it by 18, then find the number?
(A) 120
(B) 150
(C) 200
(D) 64
(E) 100
Rationale: Use the elimination method to find the correct option.
Of all the options only 120 fits
40% of 120 = 48
25% of 120 = 30
48 -30 = 18
Required number is 180.
ANSWER:A
Answer: (A) 120
Question: Among the first 1 million numbers, 40 is a number that is pretty unique.
Can you find out why ?
(A) 36
(B) 31
(C) 45
(D) 39
(E) 40
Rationale: E
40
The number 40 (Forty) is the only number in one million numbers whose letters are arranged in the order they are arranged in English alphabets as well.
Answer: (E) 40
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 22
(B) 77
(C) 18
(D) 77
(E) 65
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
Answer: C
Answer: (C) 18
Question: If l / r is an integer, which of the following statements must be true?
(A) both l and r are integers
(B) r / l is an integer
(C) r is an integer
(D) l = nr where n is an integer
(E) either l or r is negative
Rationale: Let l = 1/4; r = 1/8 --> l/r = 2
l= nr where n is an integer --> 1/4 = 2*(1/8) --> Correct
Answer: D
Answer: (D) l = nr where n is an integer
Question: Amy, Max and Nim, each have a basket full of apples. The number of apples each have is in the ratio 7:8:9 respectively. what could be the product of the number of apples.
(A) 4032
(B) 5012
(C) 1033
(D) 4123
(E) 5102
Rationale: The ratio is in in the order of consecutive positive integers. Therefore, the product of the numbers will be divisible by both 2 and 3.
4032 -> even number, 4+0+3+2=6 ->divisible by 3.
Answer:A
Answer: (A) 4032
Question: A bicyclist's wheel has a circumference of 4 meters. if the bicyclist covers 40 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.
To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.
given : x=4; y=40 and t=5
hence y/xt =40/4*5=2
Answer (A)
Answer: (A) 2
Question: How many perfect squares less than 1000 end with the digit 6?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 4:16
6:36
14:196
16:256
24:576
26:676
ANSWER:D
Answer: (D) 6
Question: 5 friends went to a restaurant and decided to pay the bill amount equally. But 4 of them could pay Rs. 50 each as a result 5th has to pay Rs. 40 extra than his share. Find the amount paid by him.
(A) 130
(B) 110
(C) 50
(D) 100
(E) None
Rationale: Explanation:
Average amount paid by 4 persons = Rs. 50
Increase in average due to Rs. 40 paid extra by the 5th men = Rs. 40/4= Rs. 10
Therefore, Average expenditure of 6 friends = Rs. 50 + Rs. 10 = Rs. 60
Therefore, Amount paid by the 6th men = Rs. 60 + Rs. 40 = Rs. 100
Correct Option: D
Answer: (D) 100
Question: A glass was filled with 40 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
(A) 0.005%
(B) 0.02%
(C) 0.5%
(D) 5%
(E) 20%
Rationale: We are given that 0.01 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20. This gives us:
0.01 x 20 = 0.2 ounces
Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:
(Amount Evaporated/Original Amount) x 100%
(0.2/40) x 100%
= 0.5%
Answer C
Answer: (C) 0.5%
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio D of the resistors’ sum of A and C to the resistors’ sum of A and B?
(A) 2(R1+R2):(R1+2R2)
(B) (R1+R2):(R1+2R2)
(C) (2R1+R2):(R1+2R2)
(D) 2(R1+R2):(2R1+R2)
(E) 2(R1-R2):(R1+2R2)
Rationale: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio D of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2+r1.A
Answer: (A) 2(R1+R2):(R1+2R2)
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
(A) 456 kms
(B) 482 kms
(C) 552 kms
(D) 556 kms
(E) 500 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.
ANSWER IS C
Answer: (C) 552 kms
Question: The dimensions of a field are 20 m by 5 m. A pit 10 m long, 4 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
(A) 1m
(B) 5m
(C) 4m
(D) 2m
(E) 3m
Rationale: The volume of the earth removed is 10*4*3 = 120 m^3.
The remaining area of the field is 20*5 - 10*4 = 60 m^2.
120 m^3 of the earth evenly spread over the area of 60 m^2 will rise the height by (height) = (volume)/(area) = 120/60 = 2 m.
Answer: D
Answer: (D) 2m
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,073 bacteria each. How many bacteria are there approximately?
(A) 10^7
(B) 10^9
(C) 10^8
(D) 10^10
(E) 10^11
Rationale: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,073 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,073=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is C.
Answer: (C) 10^8
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 32 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 3 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
11x - 32 = 7(x-1) + 3
4x = 28
x = 7
The answer is C.
Answer: (C) 7
Question: Five kg of butter was bought by a shopkeeper for 300. One kg becomes unsaleable. He sells the remaining in such a way that on the whole he incurs a loss of 10%. At what price per kg was the butter sold?
(A) 67.5
(B) 52.5
(C) 60
(D) 72.5
(E) None of these
Rationale: Let S.P. = x per kg
∴ S.P. of 4 kg = 4x
∴ 4x = 100−40/100×300
⇒ x = 270⁄4 = 67.50
Answer A
Answer: (A) 67.5
Question: If C = 2D+1 where C is an Integer then which of the following is true?
(A) C is always Odd
(B) C is always Even
(C) C is a non multiple of 2
(D) C= 1
(E) C is even if D is a non integer and a multiple of 0.5
Rationale: E
Answer: (E) C is even if D is a non integer and a multiple of 0.5
Question: A man can row upstream at 7kmph and downstream at 10kmph. Find man's rate in still water ?
(A) 8.5km/hr
(B) 6.7km/hr
(C) 5km/hr
(D) 1.5km/hr
(E) 2.6km/hr
Rationale: Rate in still water = 1/2 (10+7) = 8.5km/hr
Answer is A
Answer: (A) 8.5km/hr
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 12/5 hours
(B) 80/13 hours
(C) 30/73 hours
(D) 30/13 hours
(E) 50/13 hours
Rationale: Speed downstream = 20 + 5 = 25 kmph.
Time required to cover 60 km downstream
= d/s = 60/25
= 12/5 hours.
Answer:A
Answer: (A) 12/5 hours
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 240
(B) 340
(C) 430
(D) 450
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 4 days. In what time can the son do it alone ?
(A) 2 days
(B) 6 days
(C) 12 days
(D) 20 days
(E) None of these
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(1/4−1/5)=(5−4)/20=1/20
So son will do whole work in 20 days
Answer: D
Answer: (D) 20 days
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 6, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
(A) 600
(B) 1200
(C) 1500
(D) 1600
(E) 2000
Rationale: Sugar:Flour = 5:6 = 25:30;
Flour:Soda = 10:1 = 30:3;
Thus we have that Sugar:Flour:Soda = 25x:30x:3x.
Also given that 30x/(3x+60) = 8/1 --> x=80 --> Sugar = 25x = 2,000.
Answer: E.
Answer: (E) 2000
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?
(A) 20%
(B) 29%
(C) 70%
(D) 27%
(E) 5%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 70
2/3 SP1 = 70
SP1 = 105
100 --- 105 => 5%
Answer: E
Answer: (E) 5%
Question: A farmer has 3,000 seeds which is enough for him to plant seeds every day for 50 days. After 10 days he loses some of the seeds and the remaining seeds is now enough for him to plant for the same period of 50 days as before. How many seeds did he lose?
(A) 200
(B) 600
(C) 1,000
(D) 900
(E) 700
Rationale: 3,000 ---- 50
3,000 ---- 40
x = 50
x*50 = 3,000*40
x = 2,400
3,000
-------
600
Answer = B
Answer: (B) 600
Question: What will come in place of the x in the following Number series? 3, 6, 12, x , 33
(A) 33
(B) 37
(C) 39
(D) 21
(E) 43
Rationale: (D)
The pattern is + 3, + 6, + 9, +12 â€¦â€¦â€¦..
So the missing term is = 12 + 9= 21
Answer: (D) 21
Question: If 50% of x is 30 less than 25% of 1500, then x is?
(A) 690
(B) 860
(C) 560
(D) 875
(E) 880
Rationale: 50% of x = x/2 ; 25% of 1500 = 25/100 * 1500 = 375
Given that, x/2 = 375 - 30 => x/2 = 345 => x = 690.
Answer: A
Answer: (A) 690
Question: $600 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
(A) $100
(B) $150
(C) $125
(D) $200
(E) $240
Rationale: A:(B+C) = 2:3
A's share = 600*2/5 = $240
Answer is E
Answer: (E) $240
Question: A sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest. What is the rate of interest?
(A) 12%
(B) 11%
(C) 16%
(D) 15%
(E) 18%
Rationale: B
11%
S.I. = (19800 - 14800) = 5000.
Rate = (100 x 5000)/(14800x3)% = 11%
Answer: (B) 11%
Question: A basket contains 8 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: The total number of ways to choose 2 apples is 8C2 = 28
The number of ways that include the spoiled apple is 7C1 = 7
P(the spoiled apple is included) = 7/28 = 1/4
The answer is C.
Answer: (C) 1/4
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days will the project be completed?
(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 15 days
(E) 12 days
Rationale: Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/30).
(1/20)*(x-5) + (1/30)*(x) = 1
(x/20) + (x/30) - (5/20) = 1
5x/60 = 5/4
x = 60/4
x = 15
Therefore, the answer is D: 15.
Answer: (D) 15 days
Question: The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they subtract an antenna with a height of z feet to the top?
(A) (x+z)/2 + 37
(B) 2x−(37+z)
(C) (x−37)/2 + z
(D) x/2 - 37 + z
(E) (x−37)/2 + z
Rationale: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h1 = h2 + 37 =>
Q: h2 + z = ?
h2 + h2 + 37 = x => 2h2 = x-37 =? h2 = (x-37)/2
=> h2 - z = (x-37)/2 + z, CORRECT ANSWER E
Answer: (E) (x−37)/2 + z
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 11 cans so that at least one red and at least one blue cans to remain the refrigerator.
(A) 4
(B) 490
(C) 493
(D) 455
(E) 445
Rationale: Ways to pick 1 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 1 can out of 12 - ways to pick 1 red out of 7 red - ways to pick 1 blue out of 5 blue
12C1âˆ’7C1âˆ’5C1=12âˆ’7âˆ’1=4
ANSWER:A
Answer: (A) 4
Question: What is the area of the given rectangle?
I.	Perimeter of the rectangle is 60 cm.
II.	Breadth of the rectangle is 12 cm.
III.	Sum of two adjacent sides is 30 cm.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) II and either I or III
Rationale: EXPLANATION
From I and II, we can find the length and breadth of the rectangle and therefore the area can be obtained.
So, III is redundant.
Also, from II and III, we can find the length and breadth and therefore the area can be obtained.
So, I is redundant.
Correct answer is “II and either I or III”.
Answer E
Answer: (E) II and either I or III
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph?
(A) 22 sec
(B) 77 sec
(C) 16.7 sec
(D) 18 sec
(E) 17 sec
Rationale: D = 100 + 150 = 250
S = 54 * 5/18 = 15 mps
T = 250/15 = 16.7 sec
Answer:C
Answer: (C) 16.7 sec
Question: If d + xy = d and x is not equal to 0, which of the following must be true?
(A) x=0
(B) x+y=0
(C) x<y
(D) y=0
(E) x=d
Rationale: d + xy = d --> xy=0. Since x is not equal to 0, thus y = 0.
Answer: D.
Answer: (D) y=0
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 389$
(C) 420$
(D) 450$
(E) 489$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 60 ) =489
Hence answer will be (E)
Answer: (E) 489$