mathewhe/aqua_rat huggingface dataset:
Question: The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?
(A) Rs. 19
(B) Rs. 16
(C) Rs. 18
(D) Rs. 17
(E) Rs. 21
Rationale: Explanation:
Solution 1
Cost Price(CP) of Type 1 material is Rs. 15 per kg
Cost Price(CP) of Type 2 material is Rs. 20 per kg
Type 1 and Type 2 are mixed in the ratio of 2 : 3.
Hence Cost Price(CP) of the resultant mixture
=(30+60)/5=90/5=18
=> Price per kg of the mixed variety of material =Rs.18
Answer IS C
Answer: (C) Rs. 18
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $40,000 per year plus 15 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?
(A) 200
(B) 177
(C) 178
(D) 377
(E) 378
Rationale: Lets say she sales x items so her commission will be : x * 1500*15/100 = 225x
Salary difference is: 85000 - 40000 = 45000
So commission must at least be equal to salary difference i.e. x = 45000/225 = 200 (Approx).
Hence answer is A
Answer: (A) 200
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 87
(B) 28
(C) 26
(D) 27
(E) 25
Rationale: 36/7
r = 144
=> r = 28
Answer: B
Answer: (B) 28
Question: In a store the product A costs twice as much as the product B minus the cost of product C, If 4 products B plus 2 products C bought the price is $ 8, if 2 products you buy A plus 2 products B the price is $ 6, which is the price of the product C?
(A) 1.2
(B) 2
(C) 1.5
(D) 1.8
(E) 2.4
Rationale: We propose equations products
A = 2B-C
4B + 2C = 8 $
2A + 2B = 6 $
substituting
C = 1.2 $
Answer: A
Answer: (A) 1.2
Question: How long will a boy take to run round a square field of side 40 meters, if he runs at the rate of 12km/hr?
(A) 52sec
(B) 48sec
(C) 60sec
(D) 25sec
(E) 39sec
Rationale: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 40*4 = 160m
Time taken = 160*3/10 = 48sec
Answer is B
Answer: (B) 48sec
Question: Seven people went to a restaurant for dinner. Six of them spent $11 each on their meals and the seventh person spent $6 more than the average expenditure of all seven people. What was the total amount of money that the seven people spent?
(A) $80
(B) $81
(C) $82
(D) $83
(E) $84
Rationale: Let T be the total amount of money spent.
6*11 + (T/7 + 6) = T
72 = 6T/7
T = (7*72)/6 = 84
The answer is E.
Answer: (E) $84
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 165
(B) 178
(C) 180
(D) 198
(E) 200
Rationale: Explanation:
The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
E)
Answer: (E) 200
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 155kg then find the average weight of all the 7 rounds?
(A) 98.5 kgs
(B) 88.5 kgs
(C) 86.5 kgs
(D) 67.5 kgs
(E) 88.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 155/7 = 88.5 kgs
Answer:B
Answer: (B) 88.5 kgs
Question: Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 10 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
(A) 8 mph
(B) 5.5 mph
(C) 3.5 mph
(D) 4 mph
(E) 0.5 mph
Rationale: (1 mph +10 mph)/2 = 5.5 mph
Correct option is: B
Answer: (B) 5.5 mph
Question: Using all the letters of the word "WEDNESDAY", how many different words can be formed?
(A) A)7
(B) B)9!
(C) C)8
(D) D)7!
(E) E)3
Rationale: Explanation:
Total number of letters = 9
Using these letters the number of 9 letters words formed is 8!.
Answer: Option B
Answer: (B) B)9!
Question: If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
(A) Sunday
(B) Saturday
(C) Tuesday
(D) Wednesday
(E) None of these
Rationale: Solution
The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004. Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday (1 day before to 6th March, 2005) Answer A
Answer: (A) Sunday
Question: How many three digits number can be formed by using the digits 4,5,6,7,8,9 if the repetition of digits allowed?
(A) 106
(B) 108.
(C) 109
(D) 110
(E) 320
Rationale: For a number to be odd we must have 5,7 or 9 at the unit place. So there 3 ways of filling the unit place. Since the repetion of digits is allowed, each of the tens and hundreds place can filled in 6ways. Hence required number of numbers = 3x6x6=108. Answer : B
Answer: (B) 108.
Question: If 4<x<6<y<10, then what is the greatest possible positive integer difference of x and y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 4 < x < 6 < y < 10;
4 < x
y < 10
4 + y < x + 10
y - x <6.
Positive integer difference is 5 (for example y = 9.5 and x = 4.5)
Answer: C.
Answer: (C) 5
Question: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C. Sixty percent of students are from A, 30% from B, the rest from C, and all these students from C are freshmen. Half the student from B are upperclassman, and the rest are split evenly between the other two grades. How many sophomores are from A?
(A)  60
(B)  70
(C)  80
(D)  90
(E)  100
Rationale: Answer = B = 70
Answer: (B)  70
Question: A chair is bought for Rs.200/- and sold at Rs.320/- find gain or loss percentage
(A) 75% loss
(B) 20% gain
(C) 60% gain
(D) 30% gain
(E) 35% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (320- 200)/200 = 60% gain
C
Answer: (C) 60% gain
Question: If the selling price of 50 articles is equal to the cost price of 45 articles, then the loss or gain percent is:
(A) 45%
(B) 10%
(C) 20%
(D) 60%
(E) 56%
Rationale: C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 45.
Loss % = 5/50 * 100 = 10%
ANSWER B
Answer: (B) 10%
Question: A rectangular rug with side lengths of 6 feet and 6 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
(A) A.3/16
(B) 1/4
(C) C.1/2
(D) 7/16
(E) 7/8
Rationale: Area of the rectangular rug = 6*6 = 36
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (64 - 36)/64
= 7/16=D
Answer: (D) 7/16
Question: A car travels the first 1/2 of certain distance with a speed of 15 km/hr the next 1/4 distance with a speed of 20 km/hr, and the last 1/4 distance with a speed of 60 km/hr. the average speed of the car for the whole journey is?
(A) 12km/hr
(B) 20km/hr
(C) 89km/hr
(D) 52km/hr
(E) 79km/hr
Rationale: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/2)/15+(x/4)/20+(x/4)/60=x/y
x/30+x/80+x/240=x/y
1/20y=1
y=20km/hr
Answer(B)
Answer: (B) 20km/hr
Question: To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 75%, and reduce the price it charges its consumers by 75% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?
(A) 1. No change
(B) 2. 50%
(C) 3. 100%
(D) 4. 300%
(E) 5. 1500%
Rationale: L = 20: B = 10: H= 10 of initial box and Price = 100$
Therefore Price / cubic inch = 100 / (20*10*10) =0.05
Now, when dimensions are reduced by 75% and price also reduced by 75%
L = 5; B=2.5; H=2.5 and Price = 25$
Therefore price / cubic inch = 25 / (5*2.5*2.5) =0.8
Percentage change = (0.8 - 0.05) *100/ 0.05 = 1500%
Answer is E
Answer: (E) 5. 1500%
Question: A bag contains 4 white balls, 4 black balls, and 3 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 1/2
(B) 1/4
(C) 3/11
(D) 5/16
(E) 2/7
Rationale: The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 3/11.
The answer is C.
Answer: (C) 3/11
Question: Mahesh can do a piece of work in 40days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
(A) 45
(B) 25
(C) 37
(D) 41
(E) 60
Rationale: Work done by Mahesh in 60days = 20*1/40 = 1/2
Remaining work = 1 - 1/2 = 1/2
1/2 work is done by Rajesh in 30days
Whole work will be done by Rajesh is 30*2 = 60days
Answer is E
Answer: (E) 60
Question: Larry, Michael, and Jack have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
(A)  21
(B)  42
(C)  120
(D)  504
(E)  5040
Rationale: Larry, Michael, and Jack have five donuts to share. to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A
Answer: (A)  21
Question: X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13750 ?
(A) 3200
(B) 4000
(C) 3250
(D) 3825
(E) 3985
Rationale: Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 13750 × 16/55 = Rs.4000.
Share of Z in the profit is Rs.4000.
Option B
Answer: (B) 4000
Question: The present ages of three persons in proportions 4 : 1 : 3. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 16, 28, 35
(D) 40, 10, 30
(E) 16, 28, 33
Rationale: Let their present ages be 4x, x and 3x years respectively.
Then, (4x - 8) + (x - 8) + (3x - 8) = 56
8x = 80
x = 10.
Their present ages are 4x = 40 years, 1x = 10 years and 3x = 30 years respectively.
Answer:D
Answer: (D) 40, 10, 30
Question: If set A={4,4,4,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
(A) a) k(n+m+mn)+ k
(B) b) (1+n+m+mn)(k+1)
(C) c) k^2(mn+n/m)
(D) d) kmn(k+m+n)
(E) e) None of the above.
Rationale: a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
B
Answer: (B) b) (1+n+m+mn)(k+1)
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 60 m long and 16 1/2 m board?
(A) 99
(B) 18
(C) 16
(D) 198
(E) 15
Rationale: 60 * 33/2 = 5/2 * 2 * x => x
= 198
Answer:D
Answer: (D) 198
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
A
Answer: (A) 1
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 15% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 869 1/7 grams
(B) 869 13/23 grams
(C) 869 8/3 grams
(D) 869 1/3 grams
(E) 832 1/23 grams
Rationale: If the cost price is Rs.100, then to get a profit of 15%, the selling price should be Rs.115.
If 115kg are to be sold, and the dealer gives only 100kg, to get a profit of 15%.
How many grams he has to give instead of one kilogram(1000 gm).
115 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/115 = 869 13/23 grams.
Answer:B
Answer: (B) 869 13/23 grams
Question: If the radius of a circle is decreased 10%, what happens to the area?
(A) 10% decrease
(B) 19% decrease
(C) 36% decrease
(D) 40% decrease
(E) 50% decrease
Rationale: Area of Square = Pi* radius^2
New Radius = 0.9 * old radius
so new area = (0.9)^2 old area => 0.81 of old area =>81% old area
Ans : B
Answer: (B) 19% decrease
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 22 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 288
(B) 516
(C) 877
(D) 278
(E) 178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 22 + 21 = 43
T = 12
D = 43 * 12 = 516
Answer: B
Answer: (B) 516
Question: On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?
(A) 75
(B) 105
(C) 117
(D) 150
(E) 162
Rationale: At an average rate of 30 miles per hour in 12 minute (1/5 hours) Pat covers (distance) = (time) * (rate) = 1/5*30 = 6 miles, thus she should cover the remaining distance of 20 - 6 = 14 miles at an average rate of 8 miles per hour.
To cover 14 miles at an average rate of 8 miles per hour Pat needs (time) = (distance)/(rate) = 14/8 = 1.75 hours = 105 minutes.
Therefore Pat needs total of 12 + 105 = 117 minutes to cover the entire course.
Answer: C.
Answer: (C) 117
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 1/5 of its present?
(A) 61.5
(B) 60.5
(C) 63.5
(D) 62.5
(E) 125
Rationale: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 1x/5
Hence, number of buckets needed = 25x/(1x/5)=(25×5)/1=125
Answer is E.
Answer: (E) 125
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
A. 48 kmph
(A) 33
(B) 50
(C) 28
(D) 27
(E) 16
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer: B
Answer: (B) 50
Question: A rectangular grass field is 75 m * 40 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) s.1350
(B) s.1327
(C) s.1200
(D) s.1397
(E) s.1927
Rationale: Area = (l + b +2d) 2d
= (75 + 40 +2.5 * 2) 2*2.5 => 600
600 * 2 = Rs.1200
Answer: C
Answer: (C) s.1200
Question: Chris age after 14years will be 5 times his age 5years back. what is the present age of Chris?
(A) A)20
(B) B)25
(C) C)15
(D) D)22
(E) E)11
Rationale: Chris present age= x
after 14years = x+14
5years back = x-5
x+14= 5(x-5)
x=11
Answer is E
Answer: (E) E)11
Question: John and David were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 30 days of the festival, while David performed on 5 fewer days than John performed. If David gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y?
(A) 11Y
(B) 15Y
(C) 13Y
(D) 10Y
(E) 5Y
Rationale: Both of them were given X $ each
David to adjust Y $ in advance to John
So David now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same
So Rate of David= Rate of John
Also , David works for 25 days and John works for full 30 days
(X-Y) / 25 = (X+Y) / 30
Solving 30x-30y=25x+25y =>5x=55y => x=55/5y
X= 11Y
Answer : A
Answer: (A) 11Y
Question: When x is divided by y, the quotient is z with remainder f. Which of the following is equal to f?
(A) yz – x
(B) y/x−z
(C) x – y – z
(D) x – yz
(E) zx – y
Rationale: (x/y)=z(+f)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: (D) x – yz
Question: At the first meeting of the amputees’ support group, there were
93 fewer handshakes than there would have been if everyone
had at least one arm and shook hands once with everyone else.
The people with less than one arm made up 1/11 of the group.
How many of them were there?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: perfect example to use the units digit to get the answer quick.
let's assume the answer is A, then (22*21)/2 - (20*19)/2 = 93?
we can actually ignore the second part (after the minus) of the equation because it will always end with a units digit of 0.
the first part will have a units digit of 1 --> (units digit of 2 * units digit of 1) / 2
for the rest
B) (33*32) / 2 --> (units digit 3 * units digit 2) / 2 = 3 (success)
C) (44*43) / 2 --> (units digit 4 * units digit 3) / 2 = 6 (fail)
D) (55*54) / 2 --> (units digit 5 * units digit 4) / 2 = 0 (fail)
E) (66*65) / 2 --> (units digit 6 * units digit 5) / 2 = 0 (fail)
Interesting approach, but I don't think the unit digit is correct for B, D and E. The even number will become half and that reduced number should be used to get the unit digit.
B) (33*32) / 2 --> (units digit 3 * units digit 6) = 8
D) (55*54) / 2 --> (units digit 5 * units digit 7) = 5
E) (66*65) / 2 --> (units digit 3 * units digit 5) = 5
answer is B
Answer: (B) 3
Question: Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)).
(A) 1/50
(B) 3/50
(C) 4/50
(D) 6/50
(E) 9/50
Rationale: Answer is A.
Answer: (A) 1/50
Question: Find the missing number:
6 13 25 51 101 ?
(A) 201
(B) 202
(C) 203
(D) 204
(E) 205
Rationale: C
203
6x2+1=13
13x2-1=25
25x2+1=51
51x2-1=101
101x2+1=203
Answer: (C) 203
Question: There are 6 people in the elevator. Their average weight is 150 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
(A) 157
(B) 168
(C) 189
(D) 190
(E) 200
Rationale: Solution
Average of 7 people after the last one enters = 151 .
âˆ´ Required weight = (7x151)-(6x150)
= 1057- 900
= 157.
Answer A
Answer: (A) 157
Question: Simplify: (7+2) – (5+3+1)-1.
(A) -1
(B) –2
(C) 1
(D) 2
(E) 0
Rationale: Solution:
(7+2) – (5+3+1)-1
=9-5-3+1-1
=9-8+1-1
=2-1
=1
Answer: (C)
Answer: (C) 1
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
(A) 26
(B) 25
(C) 23
(D) 22
(E) 20
Rationale: Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140
x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer is A.
Answer: (A) 26
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(A) Rs.116.69
(B) Rs.116.60
(C) Rs.116.62
(D) Rs.116.66
(E) Rs.116.61
Rationale: Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs.116.66.
Answer: D
Answer: (D) Rs.116.66
Question: For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 253 books with me to gift her.
Can you calculate, on which day is our anniversary?
(A) 31
(B) 28
(C) 23
(D) 33
(E) 22
Rationale: E
22rd day
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 = 253
Thus our anniversary falls on the 22rd day of the month.
You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: (E) 22
Question: Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary.
What is the probability that only girls will be elected?
(A) 1/30
(B) 4/30
(C) 5/30
(D) 7/30
(E) 8/30
Rationale: GBB (girl,boy,boy)
GGB (girl,girl,boy)
GGG (girl,girl,girl)
the probability of GGG is already known - 1/30.
ANS:A
Answer: (A) 1/30
Question: The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.8,517 for a cell phone, then what was the cost price of the cell phone?
(A) Rs.5,845
(B) Rs.6,750
(C) Rs.5,700
(D) Rs.6,925
(E) None of these
Rationale: Explanation:
123% of CP =SP
Therefore, CP = Rs.8,517x100/123 = Rs.6925
Answer: Option D
Answer: (D) Rs.6,925
Question: The average expenditure of a labourer for 3 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is
(A) 70.2
(B) 50.1
(C) 75.2
(D) 78.4
(E) 52.5
Rationale: Income of 3 months = (3 × 85) – debt
= 255 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 525
Average monthly income = 525 ÷ 10 = 52.5
Answer E
Answer: (E) 52.5
Question: If a+b+c=21, what is the total number of non-negative integral solutions?
(A) 223
(B) 233
(C) 240
(D) 243
(E) 253
Rationale: Think of it is a problem of diving 21 items to three people A, B & C which may or may not receive an item.
So simply use Combination here as (n-r+1) C (r-1) i.e.
(21+3-1) C (3-1) => 23 C 2 == > 253 solutions.
ANSWER:E
Answer: (E) 253
Question: If the sum of a number and its square is 72, what is the number?
(A) 15
(B) 26
(C) 8
(D) 91
(E) none of these
Rationale: Let the number be x. Then,
x + x2 = 72
(x + 9)(x - 8) = 0
x = 8
ANSWER:C
Answer: (C) 8
Question: A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Trying to get back the number first.
5x+4
4*[5x+4] + 1
so number is 20x +17
now divide it successively by 5 and then 4
(20x + 17)/ 5 = 2 remainder and 4x + 3is number left
now divide it by 4 we will get 3 remainder
ANSWER:D
Answer: (D) 3
Question: Diesel costs Rs.4 per lit and petrol costs 6.23 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
(A) 9 months
(B) 5 months
(C) 6 months
(D) 3 months
(E) 2 months
Rationale: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85
=>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44 which is higher than the price of petrol
Answer : B
Answer: (B) 5 months