mathewhe/aqua_rat huggingface dataset:
Question: How many integers are between 2 and 57/7, inclusive?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 12
Rationale: 57/7 = 8.xx
We are not concerned about the exact value of 57/7 as we just need the integers.
The different integers between 2 and 57/7 would be 2,3, 4, 5, 6, 7, 8.
Total number of integers = 7
Option B
Answer: (B) 7
Question: In how many ways 4 Indians and 3 Englishmen can be seated in a row so that they are alternate?
(A) 120
(B) 96
(C) 144
(D) 202
(E) 256
Rationale: number of ways = 4!*3! = 144
Answer is C
Answer: (C) 144
Question: On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 45 centimeters assuming that 1-inch is 2.54 centimeters?
(A) 174.2
(B) 212
(C) 283
(D) 296
(E) 282.4
Rationale: 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 45 cm.:
45/(2.54*1.5) = x / 24 ---> x = 24*45/(3.81) = 283
Answer will be C.
Answer: (C) 283
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) 1:3
(B) 2:5
(C) 3:2
(D) 9:4
(E) 4:2
Rationale: Explanation:
Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer: Option B
Answer: (B) 2:5
Question: The sum of the ages of 4 children born at the intervals of 5 years each is 58 years. what is the age of the youngest child ?
(A) 7
(B) 8
(C) 10
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Let x = the youngest child. Each of the other four children will then be x+5, x+10, x+15
We know that the sum of their ages is 58 .
so, x+(x+5)+(x+10)+(x+15) = 58
x= 7
The youngest child is 4 years old.
Answer: A
Answer: (A) 7
Question: The average of nine numbers is 17. The average of first four numbers is 20 and the average of last four numbers is 16. What is the middle number?
(A) A)7
(B) B)8
(C) C)9
(D) D)10
(E) E)11
Rationale: The total of nine numbers = 9X17 = 153
The total of first 4 and last 4 numbers is = 4 X 20+4 X 16 = 144
So, the middle number is (153 - 144 ) = 9
C
Answer: (C) C)9
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 10 sec
(B) 30 sec
(C) 40 sec
(D) 20 s
(E) 50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 s
Answer: (D) 20 s
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $28 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: Let the weight of the package be X.
2X + 6= 28
X = 11
The answer is C.
Answer: (C) 11
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 31 8/7 years
(B) 31 5/7 years
(C) 31 5/8 years
(D) 35 5/7 years
(E) 31 3/7 years
Rationale: Required Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7 = 31 5/7 years.
Answer: B
Answer: (B) 31 5/7 years
Question: 34.96 + 240.016 + 23.98 = ?
(A) 298.956
(B) 298.694
(C) 289.496
(D) 289.469
(E) 298.964
Rationale: 34.96
240.016
+ 23.98
--------
298.956
Answer is A.
Answer: (A) 298.956
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
(A) {1, 4, 5, 10, 14}
(B) {1, 6, 7, 10, 12}
(C) {1, 5, 5, 10, 16}
(D) {1, 5, 7, 10, 18}
(E) {6, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 6 to 10 + 2*{SD} = 14.
A. {1, 4,5, 10, 14} --> only 2 numbers are in this range. Discard.
B. {1,6, 7, 10, 12} --> 4 numbers are in this range. OK.
C. {1,5, 5, 10, 16} --> only 1 number is in this range. Discard.
D. {1,5, 7, 10, 18} --> only 2 numbers are in this range. Discard.
E. {6, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.
Answer: B.
Answer: (B) {1, 6, 7, 10, 12}
Question: Mudit's age 48 years hence will be thrice his age four years ago. Find Mudit's present age?
(A) 12
(B) 19
(C) 27
(D) 18
(E) 30
Rationale: Explanation:
Let Mudit's present age be 'm' years.
m + 48 = 3(m - 4)
=> 2m = 60 => m = 30 years.
Answer:E
Answer: (E) 30
Question: The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 28
(C) 29
(D) 26
(E) 20
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 20 M + C / 2
= [(M + P) + (C - P)] / 2
= (60 + 20) / 2 = 40.
Answer:A
Answer: (A) 40
Question: In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what X percent of all the people in Smithtown are left-handed women?
(A)  50%
(B)  40%
(C)  25%
(D)  20%
(E)  10%
Rationale: looking at the ratio we can take total number of people=20..
ans 5/20 or 25% C
Answer: (C)  25%
Question: A sink has 12 liters of water some quantity of water is taken out. If the remaining water is 6 liters less then the water taken out then quantity of water taken out is.
(A) 5 liters
(B) 6 liters
(C) 7 liters
(D) 8 liters
(E) 9 liters
Rationale: Let x liter water taken out
Total=Water taken out + remaining water
12=x+(x-6)
18=2*x
x=9 liters
ANSWER:E
Answer: (E) 9 liters
Question: 10 men can cut 10 trees in 2 hours. If 2men leave the job, how many trees will be cut in 3 hours?
(A) 12
(B) 15
(C) 16
(D) 18
(E) 20
Rationale: 10 men - working 2 hrs - cut 10 trees
1men - working 1hr - cuts = 10/10*2
Thus 8 men - working 3hrs - cut = 10*8*3 / 10*2 = 12 trees
Answer is A
Answer: (A) 12
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 3456
(B) 4567
(C) 4789
(D) 5678
(E) y=5184
Rationale: Given Exp. = (12)3 x 64 = (12) 3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) y=5184
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3?
(A) 1/7
(B) 3/7
(C) 2/5
(D) 3/11
(E) 4/7
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
B
Answer: (B) 3/7
Question: Two spinning machines A and B can together produce 3,00,000 m of cloth in 10 hour, if machine B alone can produce the same amount of cloth in 15 hour, then how much cloth can machine A produce alone in 10 hour?
(A) 2,00,000 m
(B) 1,00,000 m
(C) 1,50,000 m
(D) 50,000 m
(E) None of these
Rationale: Explanation :
According to the question, machines A and B together produces 30,000 m of cloth in 1 hour.
And,machine B alone can produce 20,000 m cloth in 1 hour.
So, Machine A can produce (30,000 - 20,000) = 10,000 m cloth in 1 hour.
Hence, in 10 hour Machine A can produce 10 x 10,000 = 1,00,000 m of cloth.
Answer : B
Answer: (B) 1,00,000 m
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
(A) Saturday
(B) Monday
(C) Tuesday
(D) Friday
(E) Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday.
Answer is C.
Answer: (C) Tuesday
Question: Amy has two decks of 54 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack?
(A) 1/6
(B) 1/8
(C) 1/9
(D) 1/10
(E) 1/12
Rationale: Your solution is correct answer should be 1/12.
E
Answer: (E) 1/12
Question: What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (14^2 – 1))
(A) a. 9/19
(B) b. 10/19
(C) c. 7/30
(D) d. 11/21
(E) e. 11/19
Rationale: it can be written into
1/3+1/15+ 1/35.....1/196
i.e
1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/15)
all terms from 1/5 .. to second last term get cancelled
left with
1/3+1/6-1/30=1/2-1/30=7/30 C
Answer: (C) c. 7/30
Question: 225 mtrs long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: (A) 10
Question: Select the non termination decimal among the following.
(A) 2/5
(B) 3/4
(C) 4/5
(D) 19/3
(E) 9/10
Rationale: D. Non terminating decimal means that 19/3 = 6.3333333 and so on.
Answer: (D) 19/3
Question: The cost of 16 packets of salt,each weighing 900 grams is Rs. 28.What will be the cost of 27 packets,if each packet weight 1 kg ?
(A) Rs.52.50
(B) Rs.56
(C) Rs.58.50
(D) Rs.64.75
(E) None of these
Rationale: Solution
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
∴ (16 × 900 × x) = (27 × 1000 × 28) ⇔ x =(27x1000x28)/16x900=105/2=52.50 .Answer A
Answer: (A) Rs.52.50
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 330 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 237
(B) 287
(C) 197
(D) 660
(E) 720
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 330) = 2 + 2(extra)
=> 2x - 660 = x => x = 660.
Answer: D
Answer: (D) 660
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/2 kmph
(B) 2 2 1/8 kmph
(C) 2 2 1/0 kmph
(D) 2 2 1/2 kmph
(E) 2 2 2/2 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2 kmph
Answer: D
Answer: (D) 2 2 1/2 kmph
Question: What is the units digit of (44^4)(33^5)(21^6)?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: The units digit of 44^4 is the units digit of 4^4 which is 6.
The units digit of 33^5 is the units digit of 3^5 which is 3.
The units digit of 21^6 is the units digit of 1^6 which is 1.
The units digit of 6*3*1 is 8.
The answer is E.
Answer: (E) 8
Question: In a 8*8 chess board, what is the total number of squares refer model?
(A) 201
(B) 202
(C) 203
(D) 204
(E) 205
Rationale: 1x1 8 8 64
2x2 7 7 49
3x3 6 6 36
4x4 5 5 25
5x5 4 4 16
6x6 3 3 9
7x7 2 2 4
8x8 1 1 1
total 204
ANSWER:D
Answer: (D) 204
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 1900
(B) 1750
(C) 10300
(D) 8600
(E) 8000
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
ANSWER A
Answer: (A) 1900
Question: At a small company, 61 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?
(A) 5/16
(B) 1/3
(C) 9/20
(D) 47/61
(E) 5/7
Rationale: Lets take total employees are 100.
Given that,Total Women= 61 and Total Married = 60.
Total Men = 100 - 61 = 39 and Single men = 2/3*39 = 26.
Married men = total men - single men = 39 - 26 = 13.
Married women= Total married - Married men = 60 - 13 = 47.
Fraction of women are married = Married women / Total Women = 47 / 61 = 5/7. ANS D
Answer: (D) 47/61
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 88
(B) 28
(C) 61
(D) 86
(E) 21
Rationale: 36/7 r = 144
=> r = 28
Answer:B
Answer: (B) 28
Question: There are 45 apples and 40 oranges in stock and packs are to be filled with equal number of same type of fruits such that minimum number of packs are used. There are 20 places on the shelf to display fruits so what will be the number of empty places to display fruits?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: k is the integer that represents the number of fruit in a pack
ak= 45 --> k = 45/a
bk= 40 --> k = 40/b
45/a = 40/b --> 9b = 8a and then min (a+b) = 17
20 -17 = 3 empty shelf places
ANSWER: A
Answer: (A) 3
Question: A man can row upstream at 34 kmph and downstream at 48 kmph, and then find the speed of the man in still water?
(A) 29
(B) 92
(C) 41
(D) 32
(E) 23
Rationale: US = 34
DS = 48
M = (48 + 34)/2 = 41
Answer:C
Answer: (C) 41
Question: A and B can separately do apiece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If -the work was finished in next 4 days, then the number of days in which C alone could do the work will be
(A) 60
(B) 40
(C) 35
(D) 30
(E) 65
Rationale: A and Bs one day work= 1/20+1/15=7/60
A and Bs six day work=(7/60)*6=7/10
remaining work=1-7/10=3/10
A and Cs 4 day work=(A and Cs 1 day work)*4= (1/20+1/x)*4=3/10 (remaining work)
x=40
Cs one day work=40
ANSWER:B
Answer: (B) 40
Question: If x < y < z and y-x > 3, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
(A) 7
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: We have:
1) x<y<z
2) y-x>3
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>3, the least value for y-x must be 5, the least value for x must be 2, and, thus, the least possible value for y must be 7 (y-2=5, y=7)
2<7<z, since z is odd, the least possible value for z is 9
z-x=9-2=7
Answer A
Answer: (A) 7
Question: How long does a train 110 m long running at the speed of 54 km/hr takes to cross a bridge 132 m length?
(A) 12.9 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 16.13 sec
(E) 14.9 sec
Rationale: Speed = 54 * 5/18 = 15 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/15 = 16.13 sec.
Answer: D
Answer: (D) 16.13 sec
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 40 overs in an ideal case scenario?
(A) 1652
(B) 1651
(C) 1653
(D) 1323
(E) None
Rationale: Solution:
1323
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 39th over. In the 40th over, he can hit a six in the last ball as well as that will be the last ball of his destination.
Thus runs for the 40th over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 39 + 36 = 1323
Answer D
Answer: (D) 1323
Question: In a box of 12 pens, a total of 4 are defective. If a customer buys 3 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 1/6
(B) 2/55
(C) 14/55
(D) 12/55
(E) 3/4
Rationale: Method- 1
There are 9 fine pieces of pen and 4 defective in a lot of 12 pens
i.e. Probability of first pen NOT being defective = (8/12)
i.e. Probability of Second pen NOT being defective = (7/11)
i.e. Probability of third pen NOT being defective = (6/10)
Probability of Both pen being NON-defective = (8/12)*(7/11)*(6/10) = 14/55
Answer: option C
Answer: (C) 14/55
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2640 in all from both of them as interest. The rate of interest per annum is?
(A) 16%
(B) 12%
(C) 74%
(D) 10%
(E) 45%
Rationale: Let the rate be R% p.a. Then,
(5000 * R * 2)/100 + (3000 * R * 4)/100 = 2640
100 R + 120 R = 2640
R = 12%
Answer:B
Answer: (B) 12%
Question: Bob finishes the first half of an exam in one-seventh the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
(A) 15
(B) 24
(C) 27
(D) 36
(E) 40
Rationale: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/7's the time of the second half (7/7's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:8 and the second half is 7:8). With each eighth of an hour being 7.5 minutes (60/8), the first half of the exam would have taken 15 minutes. Correct answer is A.
Answer: (A) 15
Question: Of the students at a certain high school, 90 percent took a course in algebra or geometry and 18 percent took courses in both. If the percent of students who took a course in algebra was 2 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?
(A) 72%
(B) 70%
(C) 65%
(D) 60%
(E) 54%
Rationale: You can also just use the formula
n(A or B) = n(A) + n(B) - n(A and B)
90 = 2X + X - 18
X = 36
2X = 72
This is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 72 - 18 = 54%
Answer (E)
Answer: (E) 54%
Question: If the sides of a triangle are 30 cm, 28 cm and 14 cm, what is its area?
(A) 196 cm2
(B) 187 cm2
(C) 178 cm2
(D) 189 cm2
(E) 176 cm2
Rationale: The triangle with sides 30 cm, 28 cm and 14 cm is right angled, where the hypotenuse is 30 cm.
Area of the triangle
= 1/2 * 28 * 14
= 196 cm2
Answer: A
Answer: (A) 196 cm2
Question: If -4 < x < 7 and -7 < y < 3, which of the following specifies all the possible values of xy?
(A) -42 < xy < 21
(B) -42 < xy < 24
(C) -49 < xy < 28
(D) -24 < xy < 21
(E) -24 < xy < 24
Rationale: The least value of xy is a bit more than 7*(-7)=-49 and the largest value of xy is a bit less than (-4)*(-7)=28.
Therefore -49 < xy < 28.
Answer: C.
Answer: (C) -49 < xy < 28
Question: One cutting machine cuts 100 metal bars in 30 minutes.Another machine does the same job in 30 seconds.What time will it take if both machines are put on the same work ?
(A) 25.0 seconds
(B) 29.5 seconds
(C) 30.0 seconds
(D) 30.5 seconds
(E) 30.7 seconds
Rationale: By guess it is clear that the time taken will be less than 30 seconds and very near to it. Therefore, answer 29.5 seconds will be correct. Answer-B
Answer: (B) 29.5 seconds
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 sec. What is the length of the fast train?
(A) 38 7/6 m
(B) 38 7/4 m
(C) 38 8/9 m
(D) 38 7/9 m
(E) 38 7/7 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 7 = 350/9 = 38 8/9 m.Answer:C
Answer: (C) 38 8/9 m
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
(A) 6, 9
(B) 10, 5
(C) 7, 8
(D) 9, 6
(E) 1,5
Rationale: Explanation:
x + y = 15
2x – 3y = 5
x = 10 y = 5
ANSWER IS B
Answer: (B) 10, 5
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 10 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
(A) 7
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 10 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 10-3 = 7. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer A
Answer: (A) 7
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 20/7
(B) 20/5
(C) 20/9
(D) 20/21
(E) 20/8
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer:A:
Answer: (A) 20/7
Question: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $110. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
(A) $1
(B) $27
(C) $31
(D) $41
(E) It cannot be determined
Rationale: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:
3B+7S+C=110
4B+10S+C=164.5
Subtracting the first equation from the second gives us B+3S=54.5
Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=11. In any case, there is no necessity to know each item's price, just the sum.
Answer: A
Answer: (A) $1
Question: A discount electronics store normally sells all merchandise at a discount of 5 percent to 45 percent off the suggested retail price. If, during a special sale, an additional 2 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $400 before any discount?
(A) $215.00
(B) $200.00
(C) $215.80
(D) $182.00
(E) $215.60
Rationale: Original price : 400$
Max first discount = -45%
Thus : 400âˆ—(1âˆ’45/100)=220
Second discount on the discounted price = -2%
Thus : 220âˆ—(1âˆ’2/100)=215.60
Answer E
Answer: (E) $215.60
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 370 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 237
(B) 287
(C) 197
(D) 740
(E) 720
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 370) = 2 + 2(extra)
=> 2x - 740 = x => x = 740.
Answer: D
Answer: (D) 740
Question: Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made?
(A) 500
(B) 1000
(C) 1500
(D) 2000
(E) None of these
Rationale: C.P. for one coconut = 150⁄100 = 3⁄2
S.P. for one coconut = 2
Profit on one coconut = 2 - 3⁄2 = 1⁄2
∴ Profit on 2000 coconut = 1⁄2 × 2000 = 1000
Answer B
Answer: (B) 1000
Question: In a division sum, the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:
(A) 53
(B) 58
(C) 51
(D) 60
(E) 62
Rationale: Diver = (4*3)+2 = 14
4* Quotient = 14
Quotient = 3.5
Dividend = (Divisor * Quotient) + Remainder
Dividend = ( 14 * 3.5) + 4 = 53
A
Answer: (A) 53
Question: 85 kg of a mixture containing milk and water in the ratio 27:7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1?
(A) 10kg
(B) 7kg
(C) 5kg
(D) 9kg
(E) 3kg
Rationale: Milk in 85kg of mix = 85*27/34 = 135/2 kg
Water in it= 85-135/2 = 35/2 kg
Let x kg of water be added to it.
(135/2)/(35/2 + x) = 3/1
x=5kg
Answer is C
Answer: (C) 5kg
Question: A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5.5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 15,000
(C) 18,000
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 3 so per unit profit =3
cost to recover =45000
no of items required = 45000/3 = 15000
Ans B
Answer: (B) 15,000