mathewhe/aqua_rat huggingface dataset:
Question: Peter's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Peter's average score on the 5 tests to be 80?
(A)  80
(B)  82
(C)  84
(D)  86
(E)  88
Rationale: E. 88
Peter must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88.
Answer: (E)  88
Question: When 75% of a number is added to 75, the result is the same number. The number is
(A) 150
(B) 150
(C) 100
(D) 450
(E) None of these
Rationale: Let the number be equal to x.
3x/4 +75 = x
Hence x=300
Answer: B.
Answer: (B) 150
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?
(A) Rs.150
(B) Rs.190
(C) Rs.200
(D) Rs.250
(E) Rs.300
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
D)
Answer: (D) Rs.250
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 10%
(B) 12%
(C) 14%
(D) 20%
(E) 22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
B)
Answer: (B) 12%
Question: Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 80 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
(A) 70 miles
(B) 80 miles
(C) 90 miles
(D) 100 miles
(E) 110 miles
Rationale: Every hour, Nil gets ahead of Ethan 80 - 20 =
60 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 80 × 1 = 80 miles.
correct answer B
Answer: (B) 80 miles
Question: Solve the equation for x : 6x - 87 + 3x = 4 + 9 - x
(A) 12
(B) 5
(C) 10
(D) 9
(E) 3
Rationale: C
10
9 x + x = 13 + 87
10 x = 100 => x = 10
Answer: (C) 10
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
(A) 300 kmph
(B) 360 kmph
(C) 600 kmph
(D) 720 kmph
(E) 750 kmph
Rationale: Explanation:
Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr.
Required speed =(1200 X 3/5)km/hr	= 720 km/hr.
ANSWER IS D
Answer: (D) 720 kmph
Question: The sum P of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Pn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
(A) 4345
(B) 4302
(C) 4258
(D) 4214
(E) 4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum P of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: (D) 4214
Question: If each year the population of the country grows by 30%, how many years will elapse before the population of the country doubles?
(A) 2
(B) 4
(C) 5
(D) 3
(E) 7
Rationale: Till Year 2000, population is 100 .
Year 2001: Population becomes 130 ............. 1 Year elapsed
Year 2002: Population becomes 169 ............. 2 Year elapsed
Year 2004: Population > 200 .................. 3 year elapsed
Answer:D
Answer: (D) 3
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) Rs.1014
(B) Rs.1140
(C) Rs.999
(D) Rs.1085
(E) Rs.1020
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
ANSWER:C
Answer: (C) Rs.999
Question: John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read?
(A) 2 hours
(B) 4 hours
(C) 1 hours
(D) 5 hours
(E) 7 hours
Rationale: Mike read 5 hours. Sasha read twice as long as Mike. Hence Sasha read:
2 * 5 = 10 hours
Tom read two-fifths of the time that Sasha read. Hence Tom read:
(2 / 5) * 10 = 4 hours
John read the quarter of the time that Tom read. Hence John read:
(1 / 4) * 4 = 1 hour
correct answer C
Answer: (C) 1 hours
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
(A) 21:29
(B) 21:27
(C) 21:22
(D) 21:23
(E) 21:21
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Answer: (C) 21:22
Question: Given a certain positive integer X, if x is divided by 5 the remainder is 3 and if it is divided by 7 the remainder is 5. What is the remainder when x is divided by 30.
(A) 5
(B) Between 1 and 4, inclusive
(C) Between 5 and 10, inclusive
(D) Between 10 and 12, inclusive
(E) above 12
Rationale: Put in real numbers.
Given number x
5x+3 = 7x+5
Start 5x+3 --> 8, 13, 18, 23, 28, 33,....
Of these only 33 fit the description 7x+5. The remainder when divided by 30 is 3. So answer is B).
If there is a purely algebraic way, please tell.
Answer = B)
Answer: (B) Between 1 and 4, inclusive
Question: If f(x)=2^x and x is a natural number, what CANNOT be the answer to f(x)?
(A) 2
(B) 3
(C) 4
(D) 8
(E) 16
Rationale: There is no possible way for a 2 raised to a natural number power to be equal to 3, so the answer is B.
Answer: (B) 3
Question: A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple?
(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2
Rationale: After white,yellow, orange, green, red, blue, and purple, the next book can be of any given seven colours, therefore we have total seven possibilities, out of which we need purple i.e. 1 therefore prob is 1/7
Answer:C
Answer: (C) 1/7
Question: In the xy-coordinate system, if (m, n) and (m + 5, n + k) are two points on the line with the equation x = 2y + 5, then k =
(A) 1/2
(B) 1
(C) 2
(D) 5/2
(E) 4
Rationale: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+5 =2 *(n+k)+5.
By 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k ---> 5=2k --->k=5/2.
The answer is, therefore, (D).
Answer: (D) 5/2
Question: A and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 3,000 B's share was Rs. 1000. A's investment was
(A) s. 4,500
(B) s. 8,250
(C) s. 9,500
(D) s. 10,000
(E) s. 12,250
Rationale: A+B=15000
total profit=3000
3000-1000=2000
2000;1000=2:1
then 2*15000/3=10000
ANSWER:D
Answer: (D) s. 10,000
Question: A certain company employs 5 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?
(A) 8
(B) 24
(C) 58
(D) 40
(E) 210
Rationale: Number of ways to select 3 senior officers from 5 of them = 5C3 = 10 ways
Next we can determine the number of ways to select 1 junior officer.
number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways
Thus the number of ways to select 3 senior officers and 1 junior officer is 10 x 4 = 40 ways.
Answer: D
Answer: (D) 40
Question: If a positive odd integer N has p positive factors, how many positive factors will 5N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: I have added some extra text to make this question more GMAT-like:
Let's TEST some values of N
Try N = 3
The factors of 3 are {1, 3}. Here, p =2
So, 2N = (2)(3) = 6
The factors of 6 are {1, 2, 3, 6}. So, we have a total of4
Now check the answer choices:
A) p =2No good. We want an output of4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST another value of N
Try N = 7
The factors of 7 are {1, 7}. Here, p =2
So, 2N = (2)(7) = 14
The factors of 14 are {1, 2, 7, 14}. So, we have a total of4
Now check the REMAINING answer choices:
B) 2p = (2)(2) =4. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST one more (non-prime) value of N
Try N = 9
The factors of 9 are {1, 3, 9}. Here, p =3
So, 2N = (2)(9) = 18
The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6
Now check the REMAINING answer choices:
B) 2p = (2)(3) =6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
At this point, it SEEMS LIKELY that the correct answer is D
Answer: (D) 2p+1
Question: A certain bus driver is paid a regular rate of $16 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 $1032 in total compensation, how many total hours did he work that week?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 54
Rationale: For 40 hrs = 40*16=640
Excess = 1032-640=392
For extra hours =.75(16)=12+16=28
Number of extra hrs =392/28=98/7=14
Total hrs =40+14=54
Answer E 52
Answer: (E) 54
Question: In how many seconds will a train 180 meters long pass an oak tree, if the speed of the train is 54 km/hr?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: speed = 54 * 5/18 = 15 m/s
time = 180/15 = 12 seconds
The answer is B.
Answer: (B) 12
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 5 feet and a height of 12 feet, how far (in feet) did the oil level drop in the stationary tank?
(A) 2.5
(B) 0.025
(C) 0.05
(D) 0.03
(E) 3
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*25*12 = pi*h*100*100 (h is distance that the oil level dropped)
h = 300/10,000 = 3/100 = 0.03 ft
The answer is D.
Answer: (D) 0.03
Question: If four coins are tossed, the probability of getting two heads and two tails is ?
(A) 3/8
(B) 3/5
(C) 3/9
(D) 3/1
(E) 3/2
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: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 36 instead of 66 then find the correct average marks up to two decimal places.
(A) 72.85
(B) 74.31
(C) 72.43
(D) 73.43
(E) Cannot be determined
Rationale: Total marks = 35 x 72 =2520
Corrected total marks = 2520 - 36 + 66 =2550
Correct Average = 2550/35 = 72.85
Answer : A
Answer: (A) 72.85
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 10% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
(A) 8°
(B) 10°
(C) 18°
(D) 36°
(E) 50°
Rationale: Here all percentage when summed we need to get 100% . As per data 10+24+15+29+8 = 86%.
So remaining 14% is the balance for the astrophysics.
Since this is a circle all percentage must be equal to 360 degrees.
100% ---- 360 degrees
Then 14% will be 50 degrees..
IMO option E.
Answer: (E) 50°
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 287 cm2
(B) 384 cm2
(C) 187 cm2
(D) 167 cm2
(E) 158 cm2
Rationale: Area of a parallelogram
= base * height
= 24 * 16
= 384 cm2
Answer: B
Answer: (B) 384 cm2
Question: The cost of type 1 rice is Rs 15 per Kg and type 2 rice
is Rs 20 per Kg. If both type1 and type 2 are mixed in the
ratio of 2:3,then the price per Kg of the mixed variety
of rice is?
(A) 15
(B) 18
(C) 20
(D) 25
(E) 30
Rationale: Let the price of the mixed variety be Rs x per Kg.
Cost of 1 Kg of type 1 rice Rs 15 Cost of 1 Kg of type 2 rice Rs 20
Mean Price Rs x
20-x x-15
(20-x) /( x-15) = 2/3
=> 60-3x = 2x-30
5x = 90=>x=18.
ANSWER B
Answer: (B) 18
Question: The total age of A and B is 12 years more than the total age of B and C.C is how many years younger than A ?
(A) 12
(B) 24
(C) C is elder than A
(D) Data inadequate
(E) None of these
Rationale: Solution
(A+B)-(B + C)= 12 ⇔ A-C =12. Answer A
Answer: (A) 12
Question: At present, the ratio between the ages of Arun and Deepak is 4:5. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 17 years
(B) 15 years
(C) 18 years
(D) 12 years
(E) 25 years
Rationale: Let the present ages of Arun and Deepak be 4x and 5x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 5x
= 25 years.
Answer:E
Answer: (E) 25 years
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.3 SDs from the mean?
(A) 16
(B) 13
(C) 15
(D) 18
(E) 19
Rationale: 2.3 SD's mean is equal to: +/- 2.3*3 = +/- 6.9
ie. 13.1 to 26.9
Answer is: B
Answer: (B) 13
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 bucket is reduced to two-fifth of its present ?
(A) 52.5
(B) 62.5
(C) 72.5
(D) 82.5
(E) 81.5
Rationale: Explanation:
Let the capacity of 1 bucket = x.
Then, capacity of tank = 25x.
New capacity of bucket = 2/5 x.
Required no of buckets = 25x / (2x /5) = 62.5
ANSWER IS B
Answer: (B) 62.5
Question: A man can row a boat at 15 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/16 hours
(B) 80/13 hours
(C) 30/73 hours
(D) 30/13 hours
(E) 20/7 hours
Rationale: Speed downstream = 15 + 6 = 21 kmph.
Time required to cover 60 km downstream
= d/s = 60/21
= 20/7 hours.
Answer:E
Answer: (E) 20/7 hours
Question: Can you find the missing number in the sequence below
14 -20 34 -54 ? -144
(A) 88
(B) 77
(C) 66
(D) 55
(E) 44
Rationale: Solution:
88
Explanation:
14 -20 34 -54 ? -144
The number is difference between right number and left number.
i.e
example
14-(-20) = 34
-20-(34) = -54
34-(-54) = 88 answer
-54-(88) = -143
Answer A
Answer: (A) 88
Question: A man can row downstream at 18 kmph and upstream at 8 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 3
(B) 5
(C) 6
(D) 4
(E) 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 8 --- (2)
From (1) & (2) 2x = 26 => x = 13, y = 5. Answer: B
Answer: (B) 5
Question: In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent Z of his family’s total income?
(A)  15%
(B)  17%
(C)  24%
(D)  30%
(E)  33%
Rationale: Lets suppose the Total Family income in Feb = 100x
Wilson's earning in Feb = 40% of 100x = 40x
Earnings of remaining family in Feb = 100x - 40x = 60x
Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x
Earnings of remaining family in March = Earnings of remaining family in Feb = 60x
Thus Wilson's earning as % of Total family income in March Z= 30x/ (30+60)x = 30x/90x = 33.33%
Thus Answer is E
Answer: (E)  33%
Question: In filling a fish tank with water that is 50 m * 10 m * 1 m the volumes of water filled will be?
(A) 500 cu.m
(B) 5000 cu.m
(C) 50000 cu.m
(D) 3000 cu.m
(E) 4000 cu.m
Rationale: 50 * 10 * 1 = 500
ANSWER:A
Answer: (A) 500 cu.m
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a10 is equal to ?
(A) a. 6*2^9 -5
(B) b. 5*2^99+6
(C) c. 6*2^99+5
(D) d. 6*2^99-5
(E) e. 6*2^99-6
Rationale: Here is solution:
an+1=2an+5............(1)
lets ADD 5 to both sides....
so (an+1) + 5= 2 (an+5)....................taking 2 as common factor
now a1=1. so for n=1, an+5=6.......
putting n=1. we get both sides as,
a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)
a2= 2 *6 - 5
a2= 2 * 2 *3 - 5
a2= 2^2 *3 - 5................. so with same progression
a10= 2^10 * 3 - 5
a10=2* 2^9 * 3 - 5
a10= 6 * 2^9 - 5
A
Answer: (A) a. 6*2^9 -5
Question: 5 identical snow plows can clear an iced parking lot in 18 hours. How long would it take 6 such snow plows to clear the same parking lot?
(A) 1 hour, 15 minutes
(B) 2 hours, 30 minutes
(C) 3 hours
(D) 7 hours, 30 minutes
(E) 15 hourss
Rationale: 6/5 as many plows will take 5/6 as many hours --> 18*5/6=15 hours.
Answer: E.
Answer: (E) 15 hourss
Question: if v is a positive integer greater than 8, which of the following must be divisible by 4?
(A)  v(v-1)(v+2)(v+3)
(B)  v(v-1)(v+3)(v+4)
(C)  v(v-3)(v+2)(v+4)
(D)  v(v-3)(v+2)(v+3)
(E)  v(v+1)(v+3)(v+4)
Rationale: D.
For any integer v, D is the only answer choice which will always be divisible by 4.
A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isv* [(v-1)OR(v+3)] * [(v-2)OR(v+2)] * [(v-3)OR(v+1)]. (ANSWER D)
Answer: (D)  v(v-3)(v+2)(v+3)
Question: If a bank account has $1000 with an interest rate of 5% compounded annually, how much money will the account have after 10 years?
(A) 1629
(B) 1723
(C) 1834
(D) 1912
(E) 2012
Rationale: 1000*1.05^10=1000*1.629=1629
The answer is A.
Answer: (A) 1629
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 16 cm
(A) 304 cm2
(B) 179 cm2
(C) 285 cm2
(D) 167 cm2
(E) 197 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (16)
= 304 cm2
Answer: A
Answer: (A) 304 cm2
Question: A man engaged a servant on the condition that he would pay him Rs.800 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform?
(A) s.800
(B) s.85
(C) s.90
(D) s.100
(E) s.120
Rationale: 9/12 = 3/4 * 800 = 600
400
-------------
200
1/4 -------- 200
1 --------- ? => Rs.800
ANSWER:A
Answer: (A) s.800
Question: Two identical cubes if one of them is painted pink on its 4 sides and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting the same color is 1/3 when we roll both the cubes.
(A) 3
(B) 0
(C) 8
(D) 7
(E) 1
Rationale: Explanation:
First cube has got 4 pink sides and 2 black sides.
Let the other cube got x sides pink and (6 - x) sides black.
Now when we roll both the dice, we can either pink on both cubes or black on both cubes.
Probability = 46×x6+26×6−x6=1346×x6+26×6−x6=13
=4x+12−2x36=13=4x+12−2x36=13
⇒x=0⇒x=0
So second cube should not have any pink faces at all.
Answer:B
Answer: (B) 0
Question: The ratio of two cow A,B milk is 5:3.3kg milk of cow A get distributed and 1kg milk of cow B get distributed.now,8kg milk of cow B left.Now what is the ratio of cow A and B left milk?
(A) 3:2
(B) 4:3
(C) 5:4
(D) 6:5
(E) 5:3
Rationale: left milk of cow B=3x-1=8,3x=9,x=3.
left milk of cow A=15-3=12
12/8=3:2.
answer A
Answer: (A) 3:2
Question: The number which exceeds 16% of it by 105 is :
(A) 125
(B) 52
(C) 58
(D) 60
(E) 62
Rationale: Solution
Solution
Let the number be x.
x-16% of x =105
x-16/100x =105
x-4/25x=105
21/25x=105
x=(105x25/21)=125 Answer A
Answer: (A) 125
Question: A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
(A) 0
(B) 16
(C) 18
(D) 1
(E) 120
Rationale: suppose the no is 100
first condition if it mistakenly divided the no by 2/3 ==>100/(2/3)==>150
second condition the no should multiply by 3/2 ==> 100*3/2 ==> 150
hence output should be 150 and mistakenly the output is 150
so pecentage error is zero
ANSWER:A
Answer: (A) 0
Question: A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6}. If no digit may be repeated and each password must be at least 5 digits long, how many passwords are possible?
(A) 5! + 6!
(B) 2 x 6!
(C) 5! x 6!
(D) 11!
(E) 12!
Rationale: If we choose the 6 different digits then they can be arranged in 6! ways.
The number of possible 5-digit passwords is 6*5*4*3*2 = 6!
The total number of passwords is 6! + 6! = 2*6!
The answer is B.
Answer: (B) 2 x 6!
Question: If x = (y)(y + 1) and y is a prime number less than 7, which of the following could not be the product of 2 consecutive integers?
(A) a) 5x
(B) b) 11x
(C) c) 13x
(D) d) 30x
(E) e) 57x
Rationale: Given y is a prime number less than 7
possible values of y are 2 3 5
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
so possible values of x are 6,12,30
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 30x can be (30*31)
E. 57x cannot be
So answer option E
Answer: (E) e) 57x
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Explanation:
3x + 5x + 7x = 45
x =3
3x = 9
A)
Answer: (A) 9
Question: Joe drives 240 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?
(A) 42
(B) 51
(C) 50
(D) 54
(E) 56
Rationale: t1= 240/60=4 hours
t2=120/40=3 hours
T=t1+t2=7 hours
Avg speed = Total Distance/T
= 360/7 = 51mph=B
Answer: (B) 51
Question: In a shop 50% of the articles are sold at a profit of 20% and the remaining at a loss of 30%.what is the overall profit/loss?
(A) 15% profit
(B) 8% loss
(C) no profit, no loss
(D) 20% profit
(E) 5% loss
Rationale: 50*1.2+50*0.7/100=0.95
ANSWER:E
Answer: (E) 5% loss