mathewhe/aqua_rat huggingface dataset:
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies L and Y . The ratio of p to V in smothie L is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie L?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: The ratio of p to V in smothie L is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Answer: (D) 20
Question: A taxi company charges $1.85 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?
(A) 4 miles
(B) 4 1/4 miles
(C) 4 3/4 miles
(D) 5 1/3 miles
(E) 6 1/4 miles
Rationale: If we start out with $4.90 and have to spend $1.85 for the first quarter-mile, we will have $3.05 left to spend on quarter-mile intervals.
Since $3.05/$0.15 = 20.33, we can buy 20.33 more quarter-miles, and will travel 21.33 quarter miles in all:
21.33 × 1/4 = 5 1/3 miles.
The correct answer is choice (D).
Answer: (D) 5 1/3 miles
Question: 25,168, ? , 8176
(A) 1168
(B) 1169
(C) 1167
(D) 1166
(E) 1165
Rationale: 25*7-7 is 168.
168*7-7is1169
1169*7-7 is 8176
So 1169
ANSWER:B
Answer: (B) 1169
Question: An Olympic diver received the following scores: 7.0, 8.5, 8.0, 6.5, and 5.0. The standard deviation of her scores is in which of the following ranges?
(A) 1.01 to 1.99
(B) 2.01 to 2.99
(C) 3.01 to 3.99
(D) 4.01 to 4.99
(E) 5.01 to 5.99
Rationale: 7+8.5+8+6.5+5/5=35/5=7
∣7−7∣^2 =0^2 = 0
∣8.5−7∣^2 =1.5^2 = 2.25
∣8−7∣^2 =1^2 = 1
∣6.5−7∣^2 =0.5^2 = 0.25
∣5−7∣^2 =2^2 = 4
sqrt 2.25+1+.25+4/5 =1.22
Answer : A
Answer: (A) 1.01 to 1.99
Question: ?% of 360 = 144
(A) 277
(B) 36
(C) 64
(D) 40
(E) None of these
Rationale: ?% of 360 = 144
or, ? = 144×100/360=40
Answer D
Answer: (D) 40
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 30% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 137
(E) 210
Rationale: Set up equation:
x = total number of workers
120 = 0,3 * 2/3 * x + 0,8 * 1/3 * x
120 = 14/30 x
x = 257
257 - 120 = 137
Answer D
Answer: (D) 137
Question: A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $30000 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
(A) 5
(B) 4
(C) 9
(D) 10
(E) 15
Rationale: Since the starting point is given as the $4000 scholarship,
Assume $4000 scholarships to be x
By the given information, $2500 scholarships = 2x
and $1250 scholarships = 6x
Gievn: Total $1250 scholarships = $30000
6x*1250 = 30000
Solve for x = 4
Option B
Answer: (B) 4
Question: A rectangular garden has a 5-metre-wide road outside around all the four sides. The area of the road is 600 square metres. What is the ratio between the length and the breadth of that plot?
(A) 3 : 2
(B) 4 : 3
(C) 5 : 4
(D) Data inadequate
(E) None of these
Rationale: Area of shaded portion = 600 m.
∴ (l + 10)(b + 10) – lb = 600
or, lb + 10b + 10l + 100 – lb = 600
or, 10 (b + (l) = 500
∴ b + l = 50
From this equation we can’t get the required ratio
Answer D
Answer: (D) Data inadequate
Question: How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4?
(A) 288
(B) 173144
(C) 144
(D) 297
(E) 2181
Rationale: Explanation:
If a number has to be divisible by 4, the last two digit of that number should be divisible by 4.
So _ _ _ x y. Here xy should be a multiple of 4.
There are two cases:
Case 1: xy can be 04, 20 or 40
In this case the remaining 3 places can be filled in 4×3×2 = 24. So total 24×3 = 72 ways.
Case 2: xy can be 12, 24, 32, 52.
In this case, left most place cannot be 0. So left most place can be filled in 3 ways. Number of ways are 3×3×2 = 18. Total ways = 18×4 = 72.
Total ways = 144
Answer:C
Answer: (C) 144
Question: Which of the following CANNOT be a product of two distinct positive integers c and d?
(A) c
(B) d
(C) 3d + 2c
(D) d - c
(E) dc
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take c = 1 and d = 2 and work with the options
cd = 2
A) c take c =2, d = 1
B) d take c = 1 d = 2
C) 3d + 2c Seems tricky, lets see other options and then come back to it.
D) d - c take d = 1 and c = 2 --> d - c = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) dc Always true
You don't even have to worry what C is !
ans D
Answer: (D) d - c
Question: How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?
(A) 5 years
(B) 8 years
(C) 2 years
(D) 4 years
(E) 9 years
Rationale: D
4 years
Time = (100 x 81)/(450 x 4.5) years = 4 years.
Answer: (D) 4 years
Question: A straight pipe 1 meter in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?
(A)  1/6 and 1/4 only
(B)  1/4 and 1/3 only
(C) 1/12, 1/6 and 1/4
(D)  1/6, 1/4, and 1/3
(E)  1/12, 1/6, and 1/3
Rationale: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 3rd : 0/3, 1/3, 2/3, 3/3
Now with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12
Now comine : 0,3,4,6,8,9,12
Now find the cut with denominator 12 (Substracrt adjacent terms : 3/12, 1/12, 2/12, 1/12,3/12 i.e. 1/4, 1/12 and 1/6 after removing duplicates.
Answer - C
Answer: (C) 1/12, 1/6 and 1/4
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 33
(B) 50
(C) 88
(D) 26
(E) 23
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: (B) 50
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share?
(A) Rs.12
(B) Rs.18
(C) Rs.15
(D) Rs.21
(E) Rs.25
Rationale: Explanation :
Face value of each share = Rs.20
Dividend per share = 9% of 20 = 9×20/100=9/5
He needs to have an interest of 12% on his money
ie, Money Paid for a share 9×12/100=9/5
Money Paid for a share=9/5×100/12=15
ie, Market Value of the share = Rs.15
Answer : Option C
Answer: (C) Rs.15
Question: If x^2 - 4 = 0 and x > 0, which of the following must be equal to 0 ?
(A)  x^2 - 2x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 + 5x + 6
Rationale: x^2-4 = 0
x= +2 or x = -2
if we substitute x= 2 in the equation x^2 - 2x = 4-4 = 0
A is also the answer
Answer: (A)  x^2 - 2x
Question: If the number is divided by 3, it reduced by 42. The number is
(A) A)51
(B) B)63
(C) C)45
(D) D)40
(E) E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 42 => 2x/3 = 42
=> x = 63
Answer: Option B
Answer: (B) B)63
Question: 30 is what percent of 100?
(A) 35%
(B) 30%
(C) 45%
(D) 50%
(E) 55%
Rationale: 30/100×100=30% ANSWER : B
Answer: (B) 30%
Question: On a sum of money, the simple interest for 2 years is Rs.660, while the compound interest is Rs.696.30, the rate of interest being the same in both the cases. The rate of interest is
(A) 10%
(B) 11%
(C) 12%
(D) 10.5%
(E) None
Rationale: Solution
Difference in C.I and S.I for 2 years	= Rs(696.30-660)
=Rs. 36.30.
S.I for one years	= Rs330.
S.I on Rs.330 for 1 year	=Rs. 36.30
Rate	= (100x36.30/330x1)%
=11%.
Answer B
Answer: (B) 11%
Question: During the last four years, a large truck company purchased diesel at rates of $1.2, $1.3, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
(A) $2.5
(B) $2.55
(C) $1.52
(D) $3.25
(E) $3.0
Rationale: finding the Harmonic mean here.
HM = 4/(1/12 + 1/13 + 1/18 + 1/21) = 15.18
C
Answer: (C) $1.52
Question: If n is an integer and 101n^2 is less than or equal to 10000, what is the greatest possible value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 101 * n^2 <=10000
n^2 <=10000/101 which will be less than 100 since 10000/100 = 100 which is the square of 9
Next closest value of n where n^2<=100 is 9
Ans C
Answer: (C) 9
Question: Reema took a loan of Rs 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest.
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: Explanation:
Let rate = R% then Time = R years.
=>1200∗R∗R /100=432
=>R2=36
=>R=6%
Option B
Answer: (B) 6%
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) 7 days
Rationale: Explanation:
1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer: A
Answer: (A) 3.75 days
Question: John has 5 friends who want to ride in his new car that can accommodate only 4 people at a time (John plus 3 passengers). How many different combinations of 3 passengers can be formed from the 5 friends?
(A) 3.
(B) 8.
(C) 10.
(D) 15.
(E) 20.
Rationale: 5C3 = 10
The answer is C.
Answer: (C) 10.
Question: 57, 55, 50, 48, 43, 41, ?
(A) 30
(B) 23
(C) 36
(D) 25
(E) 32
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : C.
Answer: (C) 36
Question: which one is odd?
4377
3954
9864
8454
9831
(A) 4377
(B) 3954
(C) 9864
(D) 8454
(E) None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9864 is 27
Answer: (C) 9864
Question: x percent of y percent of z is decreased by y percent, What is the result?
(A) (100xyz - xy^3z) / 1,000,000 *(-1/48)
(B) (xz - y) / 100
(C) (xz - y) / 10,000
(D) (xyz - 2y) / 100
(E) (xyz - 2y) / 10,000
Rationale: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.
IF....
X = 10
Y = 50
Z = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.
Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 *(-1/48) = 2,500,000/1,000,000 = 2.5
This is a MATCH
A
Answer: (A) (100xyz - xy^3z) / 1,000,000 *(-1/48)
Question: I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialling the first four, then what is the chance of dialling the correct number?
(A) 1/1001.
(B) 1/1000
(C) 1/999
(D) 1/990
(E) 1/968
Rationale: Explanation :
Given, the last three digits are randomly dialled, then each of the digit can be selected out of 10 digits in 10 ways.
Hence, the required probability is:-
=>(1/10)3.
=>1/1000.
Answer : B
Answer: (B) 1/1000
Question: x an y are two truck parks 500 km apart, if a truck leaves park x at 9 a.m. and travels at a speed of 70 kmph at what time will the first truck meet the second truck which left station y at 10am and travels at a speed of 50 kmph
(A) 1.30 p.m
(B) 2.30 p.m
(C) 11.30 a.m
(D) 12.30 p.m
(E) 1.30 a.m
Rationale: Suppose they meet x hours after 9 a.m.
Distance moved by first truck in x hours + distance moved by 2nd truck in x-1 hrs = 500
70x+50(x-1) = 500
70x+50x-50= 400
120x= 450
x = 4.5
So they meet 4.5 hr after 9 a.m. which is at 1.30 p.m.
Answer is A
Answer: (A) 1.30 p.m
Question: If 40 percent of all students at college X have brown hair and 70 percent of all students at college X have blue eyes what is the difference between the minimum and maximum probability of picking a student from college X who has neither brown hair nor blue eyes?
(A) 0.2
(B) 0.3
(C) 0.4
(D) 0.6
(E) 0.7
Rationale: Max value for y = minimum of (40,70).
Because the number of students with brown hair is 40, the maximum number of students to have both brown hair and blue eyes can only be 40.
When y=40
x=30
Probability of selecting 30 students out of 100 students = 30/100 = 0.3
x will be minimum when y is minimum.
The minimum possible value for y=10
x = y-10
x=0
Because if "y" gets less than 10; the number of students get more than 100 which is not possible.
In this case; 0 students fit the criterion of not having either. Because all students have brown hair, blue eyes or both.
Probability becomes 0/100 = 0
Difference between two probabilities = 0.3-0 = 0.3
Ans: "B"
_______
Answer: (B) 0.3
Question: If John runs in the speed of 9 km/hr from his house, in what time will he reach the park which is 300 m long from his house?
(A) 2
(B) 4
(C) 5
(D) 3
(E) 6
Rationale: Speed = 9 * 5/18 = 2.5 m/sec
Time taken = 300/2.5 = 120 sec ie. 2 mins.
Answer:A
Answer: (A) 2
Question: A certain bus driver is paid a regular rate of $12 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
(A) 54
(B) 51
(C) 59
(D) 55
(E) 64
Rationale: For 40 hrs = 40*12=480
Excess = 976-480=496
For extra hours =.75(12)=9+12=21
Number of extra hrs =496/21=23.6=24 approx.
Total hrs =40+24=64
Answer E
Answer: (E) 64
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
(A) 235
(B) 451
(C) 623
(D) 215
(E) 3^5
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 3^5
Ans: E
Answer: (E) 3^5
Question: If 195,001, football shoes need to be placed in boxes and each box can contain at most 3 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:
(A) 1football shoes
(B) 3 football shoes
(C) 4 football shoes
(D) 7 football shoes
(E) 9 football shoes
Rationale: The number of football shoes that can be placed in boxes of 3 football shoes is the first number that is divisible by 3 that occurs before 195,001.
In order to divide the sum in 3 parts, the amount must be divisible by 3
Divisibility rule of 3: The sum of the digits must be divisible by 3
Sum of digits of 195,001 =1+9+5+0+0+1=16 and 1+6=7 is not divisible by 3
Hence, we need to remove 1 to this number for it to be divisible by 3
Correct Option: A
Answer: (A) 1football shoes
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 50 kmph
(B) 52 kmph
(C) 54 kmph
(D) 56 kmph
(E) 58 kmph
Rationale: Explanation:
S = 240/16 * 18/5 = 54 kmph
ANSWER IS C
Answer: (C) 54 kmph
Question: 2, -6, 18, -54, 162, (...)
(A) -486
(B) 486
(C) -428
(D) 422
(E) 423
Rationale: 2 × -3 = -6
-6 × -3 = 18
18 × -3 = -54
-54 × -3 = 162
162 × -3 = -486
Answer is A
Answer: (A) -486
Question: If the area of the equilateral triangle above is 0.75, what is the area of the adjacent square?
(A) (√3)/2
(B) √3
(C) √6
(D) 3
(E) 2√3
Rationale: Area of equilateral triangle: a^2*(square root of 3)/4 = 0.75
Hence, area of square = a^2 = 0.75 *4/ (square root of 3) = 3/ (square root of 3) = square root of 3
Answer: B
Answer: (B) √3
Question: When Robert discontinued his retainer-ship contract with a Pvt Company, management held his fees Rs. 15000/- for one month. Earlier Robert had completed a work worth fees of 7280/- from company, which was still not paid. But Robert forgot that. After one month Robert asked his fees and accountant gives Rs.18500/- to him. What is the incentive amount given to Robert?
(A) A)9500
(B) B)12500
(C) C)10780
(D) D)10500
(E) E)8600
Rationale: Total fees = Rs.15000/-
Earlier fees not paid = 7280/-
Balance Salary = 15000-7280= 7720
Paid amount = 18500/-
Incentive amount = 18500-7720 = 10780/-
Answer is C
Answer: (C) C)10780
Question: The difference between the local value and the face value of 9 in the numeral 62975148 is
(A) 899999
(B) 899991
(C) 899891
(D) 899981
(E) 899000
Rationale: Explanation:
(Local value of 9) - (Face value of 9) = (900000 - 9) = 899991
B)
Answer: (B) 899991
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1300 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) 12028
(B) 12000
(C) 12019
(D) 12197
(E) 18000
Rationale: [1300 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 18000
Answer: C
Answer: (C) 12019
Question: How many five-digit numbers exist such that the product of their digits is 400?
(A) 60
(B) 120
(C) 180
(D) 30
(E) 75
Rationale: We're asked to name all of the 5-digit numbers whose product-of-digits is 400. We can use prime-factorization to figure out the digits, BUT this comes with a "twist".....NOT ALL of the digits have to be primes....
400 = (25)(16)
The 25 = (5)(5) and there's no way around that. Every option MUST have two 5s as two of the digits.
The 16 can be broken down in a few different ways though:
16 = (1)(2)(8)
16 = (1)(4)(4)
16 = (2)(2)(4)
Each of those options has to be accounted for.
So, we have 3 sets of 5 digits:
1) 1, 2, 8, 5, 5 --> This gives us 5!/2! arrangements = 120/2 = 60 different 5-digit numbers.
2) 1, 4, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements = 120/4 = 30 different 5-digit numbers.
3) 2, 2, 4, 5, 5 --> This gives us 5!/(2!2!) arrangements = 120/4 = 30 different 5-digit numbers.
60 + 30 + 30 = 120 different 5-digit numbers
Final Answer:B
Answer: (B) 120
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
(A) 2400
(B) 2782
(C) 2097
(D) 7922
(E) 2877
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: (A) 2400
Question: Look at this series: 32, 35, 33, 36, 34, 37, ... What number should come next?
(A) 39
(B) 31
(C) 35
(D) 32
(E) 33
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
The answer is option C (35)
Answer: (C) 35
Question: Raman buys an old scooter for Rs. 5000 and spends Rs. 1000 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is :
(A) 20%
(B) 12%
(C) 10%
(D) 5%
(E) None of these
Rationale: Explanation :
Solution: C.P. =Rs. (5000+1000) =Rs. 6000; S.P. = Rs. 7200.
Gain% = (1200*100/6000) = 20%.
Answer : A
Answer: (A) 20%
Question: 8 machines, each working at the same constant rate, together can complete a certain job in 24 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 16 days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 24 to 16. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
So 3/2* 8 = 12
So we need 12-8 = 4 more machines.
Answer : C
Answer: (C) 4
Question: A wheel that has 3 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
(A) 9
(B) 10
(C) 6
(D) 8
(E) 7
Rationale: Explanation :
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
7:3::21:x => 7 * x = 21 * 3
=> x = (21 * 3)/7
=> x = 9
Answer : A
Answer: (A) 9
Question: A tour group of 25 people paid a total of $650 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) $24.7
(B) $23.94
(C) $24
(D) $25.20
(E) $30
Rationale: A.
Answer: (A) $24.7
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 321
(B) 729
(C) 451
(D) 152
(E) 451
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: B
Answer: (B) 729
Question: A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 27
Rationale: There are 4 adjacent sides for every face of the cube.
Let's say side 1 is painted red, then the 4 adjacent sides can be either green or blue alternating. This can be done in 2 ways.
GBGB
BGBG
Sixth side should be the same color as side 1.
For each color chosen for side 1(and side6) there are 2 ways of painting side 2,3,4 and 5.
No. of colors that can be chosen for side 1(and side6) is 3.
So 3*2 = 6..
ANSWER:B
Answer: (B) 6
Question: Find two consecutive integers whose sum is equal 129.
(A) 63
(B) 64
(C) 65
(D) 66
(E) 67
Rationale: Let x and x + 1 (consecutive integers differ by 1) be the two numbers. Use the fact that their sum is equal to
129 to write the equation
x + (x + 1) = 129
Solve for x to obtain
x = 64
The two numbers are
x = 64 and x + 1 = 65
We can see that the sum of the two numbers is 129.
Answer C
Answer: (C) 65
Question: Which is the smallest number divides 2800 and gives a perfect square.
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 7 is the smallest number which divides 2800 and gives a perfect square.
As 2800=2*2*2*2*5*5*7 and 7 is not in a pair which gives 400(a perfect square of 20) on dividing 2800.
ANSWER:C
Answer: (C) 7
Question: Sum of ages of two friends is 34 while difference is 2 then their ages are
(A) 18 years, 16 years
(B) 17 years, 15 years
(C) 16 years, 18 years
(D) 18 years, 16 years
(E) None
Rationale: 18,16
ANSWER:A
Answer: (A) 18 years, 16 years
Question: If 4 men working 10 hours a day earn Rs. 1600 per week, then 9 men working 6 hours a day will earn how much per week?
(A) Rs 840
(B) Rs 1320
(C) Rs 1620
(D) Rs 2160
(E) None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 1600 : x
hence 4 * 10 *x = 9 * 6 * 1600
or x = 9*6*1600/ 4*10 = 2160
Answer : D
Answer: (D) Rs 2160
Question: Two pipes P and Q can fill a cistern in 12 and 19 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/2 min
(B) 14 1/4 min
(C) 11 2/4 min
(D) 11 1/5 min
(E) 11 7/4 min
Rationale: 3/12 + x/19 = 1
x= 14 1/4
Answer: B
Answer: (B) 14 1/4 min
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours X will it take 12 beavers that work at the same pace, to build the same dam?
(A) 2.
(B) 4.
(C) X=5.
(D) X=6.
(E) 8.
Rationale: C. 5 hrs
If there were 10 beavers it qould have taken double X = 6hrs.. so closest to that option is 5.
Answer: (C) X=5.
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 64, what is the measure of side XY?
(A) 4
(B) 16
(C) 8
(D) 8√2
(E) Cannot be determined from the information provided
Rationale: ans B ..16.
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=64 or yz=8*\sqrt{2}..
therefore hyp=xy=16
Answer: (B) 16