mathewhe/aqua_rat huggingface dataset:
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 10 hrs and a machine of type S does the same job in 5 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) A)3
(B) B)4
(C) C)6
(D) D)9
(E) E)12
Rationale: Rate of machine R =1/10
Rate of machine S =1/5
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/10 +x/5 =1/2
3x/10=1/2
x=30/5=6
So no of machine R is 6
Answer C
Answer: (C) C)6
Question: What is the units digit of 18! + 2 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.
The units digit of 18! + 2 is 2.
The answer is B.
Answer: (B) 2
Question: A and B can finish a work in 14 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
(A) 33 1/3 days
(B) 35 2/3 days
(C) 33 2/3 days
(D) 31 2/3 days
(E) 32 2/3 days
Rationale: B = 1/14 – 1/24 = 5/168
=> 168/5 days
=>33 2/3 days
ANSWER:C
Answer: (C) 33 2/3 days
Question: A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 12 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
(A) 3
(B) 4
(C) 6
(D) 9/2
(E) 12
Rationale: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 12 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/12
Lets say x machines are used to attain the desired rate, thus
x/36+x/12 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+3x)/36 = 1/2
4x/36 = 1/2
x = 9/2.
QA = 9/2 (ANSWER D)
Answer: (D) 9/2
Question: Subtracting 10% from X is the same as multiplying X by what number?
(A) 97%
(B) 90%
(C) 80%
(D) 98%
(E) 20%
Rationale: X - (10/100) X = X * ?
? = 90%
Answer: B
Answer: (B) 90%
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red?
(A) 2/13
(B) 3/17
(C) 5/26
(D) 5/21
(E) 7/15
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: How many words, with or without meaning, can be formed using all letters of the word SHARP using each letter exactly once?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: The Word SHARP has exactly 5 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 5 letters taken all at a time.
= P (5, 5) = 5!
= 5 x 4 x 3 x 2 × 1
= 120
ANSWER:D
Answer: (D) 120
Question: In a college the ratio of the numbers of boys to the girls is 8:5. If there are 210 girls, the total number of students in the college is?
(A) 562
(B) 356
(C) 452
(D) 416
(E) 546
Rationale: Let the number of boys and girls be 8x and 5x
Then , 5x = 210
x= 42
Total number of students = 13x = 13*42 = 546
Answer is E
Answer: (E) 546
Question: Which one of the following is a composite number?
(A) 31
(B) 61
(C) 71
(D) 73
(E) 55
Rationale: 55 is divisible by 5,11,55. So, it a composite number.
E
Answer: (E) 55
Question: Akash leaves Chennai at 6am & reaches Bangalore at 10am. Prakash leaves Hyderabad at 8 am and reaches Chennai at 11:30 am. At what time do they cross each other?
(A) 5 : 54am
(B) 6 : 56am
(C) 8 : 56am
(D) 9 : 56am
(E) 10 : 26am
Rationale: Time taken by Akash = 4 h
Time taken by Prakash = 3.5 h
For your convenience take the product of times taken by both as a distance.
Then the distance = 14km
Since, Akash covers half of the distance in 2 hours(i.e at 8 am)
Now, the rest half (i.e 7 km) will be coverd by both prakash and akash
Time taken by them = 7/7.5 = 56 min
Thus , they will cross each other at 8 : 56am.
C
Answer: (C) 8 : 56am
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
(A) 12
(B) 15
(C) 21
(D) 36
(E) 42
Rationale: Since here order of socks is not important then we'll have 7C2 i.e. 21 combinations.
If order is important then we would have got 42 socks...
ANS option C is correct answer..
Answer: (C) 21
Question: if the average of 6 consecutive number is 27, then the largest of the number is?
(A) 27.5
(B) 28.5
(C) 29
(D) 29.5
(E) 30
Rationale: x+x+1+x+2+x+3+x+4+x+5/6=27
6x+15=162
x=24.5
x+5=29.5
ANSWER:D
Answer: (D) 29.5
Question: Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?
(A) Rs. 1100
(B) Rs. 500
(C) Rs. 1200
(D) Rs. 700
(E) None of these
Rationale: Explanation:
Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 - (p + q) => r = Rs.500.
ANSWER IS B
Answer: (B) Rs. 500
Question: For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 5| + |-b| + |b – a| + |ab| =
(A) a-b
(B) 2a-2b
(C) 2a-2b-5
(D) ab + 2b + 5
(E) a-b-5
Rationale: Observation-1: |a – b| = b – a
which is possible only when signs of a and b are Same
Since Given a > 0
so we figure out that a and b are both positive
Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a
Now you may choose the values of a and b based on above observations
e.g. b = 5 and a=1 and check the value of given functions and options
|a + 5| + |-b| + |b – a| + |ab| = |1 + 5| + |-5| + |5 – 1| + |1*5| = 20
ab + 2b + 5= 1*5+10+5=20
all other options are not equal to 20
Answer : D
Answer: (D) ab + 2b + 5
Question: In a can, there is a mixture of milk and water in the ratio 1 : 5. If it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 2 : 5. Find the capacity of the can?
(A) 14
(B) 44
(C) 48
(D) 50
(E) 56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 1/6 (T - 2)
After adding milk, quantity of milk in the mixture = 2/7 T.
2T/7 - 2 = 1/6(T - 2)
5T = 84 - 14 => T = 14.
Answer:A
Answer: (A) 14
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
(A) 621
(B) 276
(C) 236
(D) 600
(E) 211
Rationale: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Answer: D
Answer: (D) 600
Question: Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is:
(A) 1 : 2
(B) 2 : 3
(C) 3 : 2
(D) 19: 135
(E) None of these
Rationale: Explanation:
This question can be solved using weighted average formula. If two quantities of weights m, n have concentrations x, y are mixed then, final concentration = mx+ny/m+n
Take 1 unit of gold and x units of copper.
1×19+x×9/1+x=15⇒19+9x=15+15x
⇒x=2/3
So they are to be mixed in the ratio 1 : x = 1:2/3 or 3 : 2
Correct Option: C
Answer: (C) 3 : 2
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
(A) 4 months
(B) 5 months
(C) 6 months
(D) 8 months
(E) 9 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.ANSWER D
Answer: (D) 8 months
Question: The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 215 m
(C) 245 m
(D) 250 m
(E) 270 m
Rationale: Let the length of the bridge:L
The equation now is L+160/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =215m
ANSWER:B
Answer: (B) 215 m
Question: In 1950, John was 4 times as old as Tom. In 1955, Richard was 3 times as old as Tom. In which year was John twice as old as Tom?
(A)  1960
(B)  1970
(C)  1972
(D)  1975
(E)  1980
Rationale: In 1950: Jo = 4 To-------------- eq1
In 1955: Jo +5 = 3(To+5)---------eq2
Thus in 1950, solving eq1 and eq2
Jo = 10 , Jo =40
Now for each year we can calculate:
1960: Jo = 50 , To=20
1965: Jo = 55, To=25
1970: Ri= 60, Ro = 30
Thus Ans:B
Answer: (B)  1970
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of thesportformulation contains 5 ounces of corn syrup, how many ounces of water does it contain?
(A) 15
(B) 30
(C) 45
(D) 75
(E) 90
Rationale: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 5.
So, x = 325 / 4 ounces.
Water = (60 / 65) * (325 / 4) = 60 * 3 / 4 = 75 ounces.
Ans D
Answer: (D) 75
Question: Alice has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Alice, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Alice has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.
(A) None
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: Let Alice, Doris and jane have A, D and J stamps initially.
We know that
A =3D
and
J=d+7
After addition of 4 stamps they'll have A+4, D+4, and J+4 stamps respectively.
Lets analyze each statements:
Alice has more stamps than Jane.
this can be written as
A+4 > J+4
=> 3D+4 > D+7+4
=>D >7/3
It may not be true for many values of D.. D could very well be equal to 1,2 etc for which D<7/3. Not correct.
Jane has 3 more stamps than Doris.
this can be written as
J+4 = (D+4)+3
=> D+7+4 = D+4+3
Clealy not correct for any value of D.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.
(A+4)+(D+4) = 4k, where k is any integer
=> 3D+4+D+4 =4k
=> 4D+8 = 4K
=> 4(D+2) = 4K
or K = D+2 .. clearly possible for any value of D. Hence Correct.
Hence Ans B. Only iii is correct.
Answer: (B) III only
Question: What is the thousandths digit in the decimal equivalent of 43/5000?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 8
Rationale: 43/5000 = 43 /(5*10^3)
= (43/5) *10^-3
=8.6 * 10^-3
=.0086
Thousandths digit = 8
Answer E
Answer: (E) 8
Question: Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture?
(A) 1 : 9
(B) 1 by 5
(C) 1 : 7
(D) 1 : 3
(E) 1 : 1
Rationale: Selling price of the mixture = 70 and profit = 20%
Cost price of the mixture = 70×100120=70×5670×100120=70×56
By applying alligation rule:
So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5
Answer:B
Answer: (B) 1 by 5
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 999
(B) 279
(C) 120 metre
(D) 99
(E) 21
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/ sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Answer: (C) 120 metre
Question: A certain experimental mathematics program was tried out in 2 classes in each of 34 elementary schools and involved 40 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
(A) 0 and 13
(B) 0 and 14
(C) 1 and 10
(D) 1 and 9
(E) 2 and 8
Rationale: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (34*2=68), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (68-40=28). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 28/2 = 14. So the greatest possible value of the # of teachers who had 3 classes is 14.
Only answer B has this option.
Answer: (B) 0 and 14
Question: In a pair of fractions, fractions A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
(A) 1/5
(B) 1/25
(C) 2/5
(D) 3/5
(E) Data inadequate
Rationale: a=2b
ab=2/25
2b*b=2/25
b^2=1/25
b=1/5
a=2/5
ANSWER:C
Answer: (C) 2/5
Question: A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
(A) 5 kmph
(B) 4 kmph
(C) 4.75 kmph
(D) 4.95 kmph
(E) 4.65 kmph
Rationale: Speed Downstream = 22/4 = 5.5 kmph
Speed Upstream = 22/5 =4.4 kmph
Speed of the boat in still water = 5.5+4.4/2=4.95 kmph
Answer : Option D
Answer: (D) 4.95 kmph
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
(A) 814 tiles
(B) 800
(C) 100
(D) 200
(E) 456
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/41 x 41 = 814.
Answer:A
Answer: (A) 814 tiles
Question: The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =
(A) 18
(B) 29
(C) 37
(D) 44
(E) 51
Rationale: Option B & C can be ruled out as they themselves are prime numbers
18 = 2*9 = 3*6 >> Ignore
44 = 2 * 22 = 4 * 11 >> Ignore
51 = 3*17 >> Answer
Answer E
Answer: (E) 51
Question: In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions?
(A) 63
(B) 48
(C) 85
(D) 52
(E) 47
Rationale: In the given word there 6 letters in that there are 2 vowels and 4 consonants
no of ways of arranging the vowels=2p2=2
no of ways of arranging the consonants=4p4=24
total number of ways 24*2=48
Answer(B)
Answer: (B) 48
Question: Evaluate (51 + 52 + 53 + ... + 100)
(A) 3775
(B) 3665
(C) 3456
(D) 3459
(E) 3569
Rationale: Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775.
Option A
Answer: (A) 3775
Question: The sum of two consecutive integers is 31. Find the numbers.
(A) 17, 18
(B) 7, 8
(C) 15, 16
(D) 1, 2
(E) 8, 9
Rationale: n + (n + 1) = 31
2n + 1 = 31
2n = 30
n = 15
Answer: C
Answer: (C) 15, 16
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 20
(B) 80
(C) 100 students
(D) 200
(E) 120
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10
x - y = 20 .... (i)
and x + 20 = 2(y - 20)
x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
ANSWER:C
Answer: (C) 100 students
Question: A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
(A) 720
(B) 760
(C) 680
(D) 780
(E) 880
Rationale: On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is
10 x 9 x 8 = 720
ANSWER:A
Answer: (A) 720
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 8 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
(A) $115
(B) $101
(C) $100
(D) $108
(E) $109
Rationale: Final price = (1+8/100) * Original Price
= 1.08* Original Price
From options given only 108 is divisible by 1.08 as it is stated OP is whole dollar amount.
Hence D
Answer: (D) $108
Question: A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?
(A) 276 Marks
(B) 200 Marks
(C) 186 Marks
(D) 187 Marks
(E) 167 Marks
Rationale: 30% ------------ 50
45% ------------ 25
----------------------
15% ------------- 75
30% -------------- ?
150 + 50 = 200 Marks
Answer: B
Answer: (B) 200 Marks
Question: In a barrel of juice there is 30 liters; in a barrel of beer there are 50 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:3.
(E) 15:4
Rationale: Price of 30 L juice= 3x
1L= 3x/30
Price of 50 L beer= 4x
1L= 4x/50
Ratio of 1 L price = 3x/30/4x/50= 15:4
E is the answer
Answer: (E) 15:4
Question: If four coins are tossed, the probability of getting two heads and two tails is?
(A) 3/8
(B) 3/9
(C) 3/7
(D) 3/56
(E) 3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A
Answer: (A) 3/8
Question: Barbara has 8 shirts and 10 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
(A) 41
(B) 66
(C) 36
(D) 70
(E) 84
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (10-3) pants
2*7=14
we can combine the other shirts (6) with any pants (9)
7*10=70
Thus total :70+14=84	ANS:E
Answer: (E) 84
Question: A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $24
(D) $25.20
(E) $30
Rationale: Soln:-
630/25=x+0.05x
630/25=1.05x
x=(630*100)/(25*105)
=63*10*4/21*5=24
ANSWER:C
Answer: (C) $24
Question: After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount
(A) 38%
(B) 15%
(C) 20%
(D) 12%
(E) 36%
Rationale: Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
x=(100-80)=20
first discount = 20%
Ans: C
Answer: (C) 20%
Question: A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?
(A) 9
(B) 18
(C) 12
(D) 20
(E) 16
Rationale: Explanatory Answers
The father completes the job in x hours.
So, the son will take 2x hours to complete the same job.
In an hour, the father will complete 1/x of the total job.
In an hour, the son will complete 1/2x of the total job.
So, if the father and son work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.
The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6<sup>th</sup> of the task in an hour.
Equating the two information, we get 3/2x = 1/6
Cross multiplying and solving for x we get 2x = 18 or x = 9.
The father takes 9 hours to complete the job.
Answer A
Answer: (A) 9
Question: A 2-year certificate of deposit is purchased for Q dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
(A) k(1.06)^2
(B) k(1.06)^8
(C) k(1.015)^2
(D) Q(1.015)^8
(E) k(1.03)^4
Rationale: Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus Q(1.015)^8
Answer: D
Answer: (D) Q(1.015)^8
Question: Walking 6/5 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 22
(B) 99
(C) 27
(D) 24
(E) 20
Rationale: Speed Ratio = 1:6/5 = 5:6
Time Ratio = 6:5
1 -------- 6
4 --------- ? 24 m.Answer:D
Answer: (D) 24
Question: 12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work?
(A) 10 days
(B) 9 days
(C) 8 days
(D) 7 days
(E) 6 days
Rationale: total work 12*18=216 units
after 6 days work finished 6*12=72 units
remaining work 216-72=144 units
remaing days =144(12+4)=9 days
ANSWER:B
Answer: (B) 9 days
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 25% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
(A) 135.7%
(B) 129.6%
(C) 123.5%
(D) 117.4%
(E) 112.6%
Rationale: 0.75*1.2^3 = 1.296
The answer is B.
Answer: (B) 129.6%
Question: If 0 < a < b and k = (2a + 6b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 8
(D) k > 9
(E) k > 11
Rationale: Here's another approach:
k = (2a + 6b)/b
= 2a/b + 6b/b
= 2(a/b) + 6
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 6
From here, we can see that k must be less than 8
Answer: C
Answer: (C) k < 8
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.78 less, he could have gained 25%. What is the cost price?
(A) s.370
(B) s.375
(C) s.375
(D) s.390
(E) s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
78 ----- ? => 390
ANSWER:D
Answer: (D) s.390
Question: If 25% of a number exceeds 8% of it by 11.9, then find the number?
(A) 76
(B) 70
(C) 55
(D) 65
(E) 22
Rationale: Use the elimination method to find the correct option.
Of all the options only 70 fits
25% of 70 = 17.5
8% of 70 = 5.6
17.5 - 5.6 = 11.9
Required number is 70.
ANSWER:B
Answer: (B) 70
Question: A CAR MOVES AT THE SPEED OF 80KM/HR. WHAT IS THE SPEED OF THE CAR IN METRES PER SECOND?
(A) 8 m/sec
(B) 20 1/9 m/sec
(C) 22 2/0 m/sec
(D) Cannot be determined
(E) None of these
Rationale: SPEED = (80*5/18)M/SEC=200/9 M/SEC = 22 2/9 M/SEC.
CORRECT OPTION: C
Answer: (C) 22 2/0 m/sec
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
(A) 5/8
(B) 5/9
(C) 5/1
(D) 5/3
(E) 5/2
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216
=5/9.
Answer:B
Answer: (B) 5/9