divelab/Sys2Bench huggingface dataset:
Question: For all numbers l and m, the operation @ is defined by l@m = l^2 - lm. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
Options:
A)II
B)I and II
C)I and III
D)II and III
E)All of the above
Rationale: l@m= l^2 - lm=l(l-m).... so l@m will be zero if l=m or l=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible
only l and ll possible
answer: B
Answer: B
Question: An investment with the Brown company yields 10% compounded annually over 2 years, while an investment with Green Crop. yields 20% annually over the same period. If Fernando invests a given amount in Green Corp, by what percent should Rita's initial investment exceed Fernando's, if she wants to invest in Brown but match the final value of his investment?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Let Brown company's investment be b;
After 1 year = 1.1b
After 2 years = 1.1*1.1b = 1.21b
Let Green corp's investment be g;
After 1 year = 1.2g
After 2 years = 1.2g*1.2 = 1.44g
1.21b = 1.44g
b = (1.44/1.21)g = 1.19g(approx)
The answer is indeed 19%.
ANSWER:D
Answer: D
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 12 minutes less than they can row it in still water. How long would they take to row down with the stream
Options:
A)45 or 23 minutes
B)63 or 12 minutes
C)72 minutes
D)19 minutes
E)25 minutes
Rationale: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-12))
giving t = 72
C.
Answer: C
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
Options:
A)23 minutes
B)30 minutes
C)43 minutes
D)23 minutes
E)33 minutes
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer:B
Answer: B
Question: If 8 spiders make 4 webs in 9 days, then how many days are needed for 1 spider to make 1 web?
Options:
A)10
B)20
C)12
D)16
E)18
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)8:1
(webs) 1:9}::x:4
â‡’8Ã—1Ã—9=1Ã—4 Ã— x
â‡’x=18
Answer: Option E
Answer: E
Question: Eight participants are participating in a competition. In how many ways can the first three prizes be won?
Options:
A)920
B)680
C)820
D)336
E)620
Rationale: Out of 8 participants, the first three prizes can be won in,
8P3 = 8! / (8 - 3)!
= 8 x 7 x 6
= 336 ways
ANSWER:D
Answer: D
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
Options:
A)37.2%
B)37.5%
C)30.2%
D)37.7%
E)33.2%
Rationale: Explanation:
100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
Answer: Option B
Answer: B
Question: An bus covers a certain distance at a speed of 220 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
Options:
A)600 km/hr
B)660 km/hr
C)730 km/hr
D)750 km/hr
E)760 km/hr
Rationale: Distance = (220 x 5) = 1100 km.
Speed = Distance/Time
Speed = 1100/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1100 x 3 km/hr = 660 km/hr.
B
Answer: B
Question: A person travelled from his house to office at 30km/hr and office to house at 10km/hr. Then find the average speed?
Options:
A)15km/hr
B)20km/hr
C)32km/hr
D)24km/hr
E)25km/hr
Rationale: Average speed = (2*30*10)/(30+10)
= 15km/hr
Answer is A
Answer: A
Question: Which of the following is not a leap year ?
Options:
A)700
B)800
C)900
D)1000
E)1200
Rationale: The century divisible by 400 is a
answer :A
Answer: A
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
Options:
A)20
B)23
C)25
D)21
E)22
Rationale: Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
Answer is C.
Answer: C
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 5 minutes 20 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
Options:
A) 3%
B) 50%
C) 8%
D) 10%
E) 12%
Rationale: Bob's time = 640 secs.
His sis' time = 320 secs.
Percent increase needed = (640-320/640) * 100 = 320/640 * 100 = 50%. Ans (B).
Answer: B
Question: In a 1 km race, A beats B by 28 meters in 7sec. Find A's time over the course?
Options:
A)4min,9sec
B)4min,3sec
C)4min,7sec
D)3min,3sec
E)5min,3sec
Rationale: Explanation:
B covers 28 meters in 7sec. So, B's time over the course = =250 sec.
Whereas A's time over the course = 250 -7 = 243 sec.
i.e A's time over the course is 4min , 3 sec.
Answer: B) 4min,3sec
Answer: B
Question: If Rs.480 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Options:
A)s.575
B)s.595
C)s.590
D)s.570
E)s.585
Rationale: 80 = (480*4*R)/100
R = 3.125%
I = (480*6*3.125)/100 = 90
480 +90 = 570
ANSWER:D
Answer: D
Question: 42 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
Options:
A)28
B)77
C)36
D)25
E)13
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
27 : 42 :: 18 : x
[Please pay attention, we have written 27 : 42 rather than 42 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
{\color{Blue} x=\frac{42\times 18}{27}}
x = 28
So 28 days will be required to get work done by 27 men.
Answer: A
Answer: A
Question: If 25% of x is 15 less than 15% of 1500, then x is?
Options:
A)872
B)738
C)837
D)840
E)83
Rationale: 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 15
=> x/4 = 210 => x = 840.
Answer:D
Answer: D
Question: A can complete a work in 12days and B can do the same work in 8days. If A after doing 2days, leaves the work, find in how many days B will do the remaining work?
Options:
A)2days
B)4 1/2days
C)6 1/2 days
D)7 3/4days
E)10days
Rationale: The required answer = (12-2)*8 / 12 = 80/12 = 6 1/2days
Answer is C
Answer: C
Question: Mangala completes a piece of work in 15 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)10 days
B)12 days
C)14 days
D)16 days
E)18 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 15 × 30/45 = 10 days
A)
Answer: A
Question: If the simple interest on a sum of money at fifteen percent per annum for four years is Rs.9000, compound interest on the same sum for the same period at the same rate of interest is
Options:
A)10,250.50
B)12,010.50
C)12,250.00
D)10,012.50
E)13,626.50
Rationale: S I for 4 years = 9000 ie for one year =2250
The compound interest for Rs.2250 for the next three years = 2250(3)=6750, 6750*15/100 = 1012.50
The CI for four years 9000+1012.50 = 10,012.50
ANSWER:D
Answer: D
Question: A total of 22 men and 30 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
Options:
A) 31
B) 31.5
C) 32.8
D) 32.5
E) 33
Rationale: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 52 = 22 * 38 + 30 * Aw
=>1820 = 836 + 30 Aw
=> 30 Aw = 984
=>Aw = 32.8
Answer C
Answer: C
Question: A school having four classes only have student strength of 10, 20, 30 and 40 respectively. The pass percentages of these classes are 80%, 30%, 60% and 90% respectively. What is the pass percentage for the entire school?
Options:
A)56%
B)76%
C)34%
D)68%
E)46%
Rationale: 80% of 10+30% of 20+60% of 30+90% of 40
=8+6+18+36 =
now 68 of 100
= 68%
ANSWER:D
Answer: D
Question: How many two cent stamps are there in a dozen?
Options:
A)14
B)11
C)25
D)12
E)19
Rationale: D
12, a dozen of anything is still 12!
Answer: D
Question: Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.
Options:
A)12 min
B)25 min
C)40 min
D)48 min
E)52 min
Rationale: Distance = Speed * time
4*11/4 = 11km
New Speed = 16.5 kmph
Therefore time = D/S = 11/16.5 = 40min
Answer : C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
Options:
A)118
B)150
C)300
D)258
E)191
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 18 = 300 m
Answer: C
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)A)150m
B)B)270m
C)C)180m
D)D)158m
E)E)350m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 250/20
4X + 480 = 3X + 750
X = 270m
Answer: B
Answer: B
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability A that all three secretary are assigned at least one report?
Options:
A)8/9
B)64/81
C)4/9
D)16/81
E)5/9
Rationale: For each report there are three possible outcomes: Secretary A, Secretary B, Secretary C
Total outcome: 3^3=27
Total outcome that three secretary are assigned at least one report: P(3,3)=3!=6
Probability A= 6/27=2/9.C
Answer: C
Question: A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
Options:
A)13
B)10
C)16
D)50
E)23
Rationale: Option B
Explanation:
A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: B
Question: Nilesh sold an item for Rs.6400/- and incurred a loss of 20%. At what price should he have sold the item to have gained a profit of 20%?
Options:
A)Rs.7800
B)Rs.9600
C)Rs.8750
D)Rs.8760
E)None of these
Rationale: Explanation:
20% loss means SP = 80% of CP
:. CP = Rs.6400x100/80 = Rs.8000.
The SP for a gain of 20% = 8000+20% of 8000 = 8000+1600 =Rs9600.
Answer: Option B
Answer: B
Question: Which expression is the greatest
Options:
A)3852/3857
B)3456/3461
C)3591/3596
D)3346/3351
E)3453/3458
Rationale: Options can be re-written as (x-5)x => 1-(5/x)
A) 1- (5/3857)
B) 1- (5/3461)
C) 1- (5/3596)
D) 1- (5/3351)
E) 1- (5/3458)
To get the largest among these second half should be the least and so denominator to be largest. Hence 'A'.
Answer: A
Question: The least number which when increased by 3 each divisible by each one of 24, 32, 36 and 54 is :
Options:
A)427
B)859
C)869
D)861
E)None of these
Rationale: Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 3 = 864 - 3 = 861. Answer D
Answer: D
Question: The average of 8 numbers is 21. If each of the number is multiplied by 8, the average of the new set of numbers is :
Options:
A)168
B)667
C)288
D)1991
E)111
Rationale: Average of new numbers = (21×8)=168
Answer:A
Answer: A
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,814,477 minutes earlier? (Assume standard time in one location.)
Options:
A)6:41
B)6:35
C)6:33
D)6:30
E)6:27
Rationale: 6:27 minus 2,814,477 in any way must end with 0.
The only answer choice which ends with 0 is D.
The answer is D.
Answer: D
Question: The sum of 3 hours 45 minutes and 1 hours 55 minutes is approximately what percent of a day?
Options:
A)21%
B)22%
C)23%
D)24%
E)25%
Rationale: Since the question is asking for an approximate percentage
3:45+1:55 ~ 6 hours
% of day = 6*100/24 ~ 6*100/25= 24%
Answer is D.
Answer: D
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. 60 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.2 years and the standard deviation is 2.8 years, what percent of the distribution has more than 10.0 years as a shelf’s average life?
Options:
A)10%
B)12%
C)14%
D)15%
E)17%
Rationale: Average = 7.2
SD = 2.8
7.2 - 2.8 < 60% of distribution < 7.2 + 2.8
4.4 < 60% of distribution < 10.0
30% is outside this range.
Given: Distribution is symmetric. So 15% of distribution is less than 7.5 and the other 15% of distribution is greater than 10.0.
Answer: D
Answer: D
Question: If x represents the sum of the interior angles of a regular hexagon and y represents the sum of the interior angles of a triangle, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?
Options:
A)Triangle
B)Square
C)Rhombus
D)Trapezoid
E)Pentagon
Rationale: Sum of angles of Hexagon = 180*(6-2) = 720 => using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon
Sum of angles in triangle = 180*(3-2) =180
Difference = 720 - 180 = 540 => Pentagon
hence (E).
Answer: E
Question: Given that a “16-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 16-inch pizza gives you approximately what percent increase in the total amount of pizza?
Options:
A)33
B)50
C)67
D)180
E)300
Rationale: area of 8 inch pizza= 4*4*pi=16 pi
area of 16 inch pizza =8*8*pi=64 pi
48/16*100=300% increase
hence answer is E
Answer: E
Question: What is the sum of the integers from -185 to 195 inclusive?
Options:
A)0
B)5
C)375
D)1905
E)965
Rationale: sum/n= average.
sum=(average)(n)
average=a+b/2=-185+195/2=5
number of items(n)=B-A+1=195-(-185)+1=195+186=381.
sum=average*n=5*381=1905.
answer is D
Answer: D
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
Options:
A)500
B)520
C)600
D)300
E)250
Rationale: 70 = (P*4*7/2)/100
P = 500
ANSWER A
Answer: A
Question: At a contest with 500 participants, 1/2 of the people are aged 28 to 32. Next year, the number of people aged 28 to 32 will increase by 1/8. After this change, what percentage of the total 500 people will the 28- to 32-year-olds represent?
Options:
A)33.25%
B)40.25%
C)50.25%
D)55.25%
E)56.25%
Rationale: I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 500 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/8, we are multiplying it by 1 + 1/8 = 9/8, so the answer here must be (1/2)*(9/8) = 9/16 = 56.25 %.
Answer is E
Answer: E
Question: If t and y are both odd prime numbers and t < y, how many distinct positive integer factors does 2ty have?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: Since 2ty prime factors are t^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: D
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 16 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
Options:
A) 3
B) 6
C) 7
D) 7.8
E) 9
Rationale: Answer is C.
x/x+36=1/5
x=9
16-9=7
Answer: C
Question: Which of the following equations has a solution in common with x^2 - 6x + 9 = 0?
Options:
A)x^2 + 4x +4 = 0
B)3x^2 + 10x + 3 = 0
C)x^2 + 2x - 3 = 0
D)3x^2 + 17x - 6 = 0
E)none of the above
Rationale: Given : x^2 - 6x + 9 = 0 => (x-3) (x-3) = 0 => 3 (both 3s) is the only roots.
A. x^2 + 4x +4 = 0 => (x+2) (x+2)
B. 3x^2 + 10x + 3 = 0 => (3x+1) (x+3)
C. x^2 + 2x - 3 = 0 => (x+3) (x-1)
D. 3x^2 + 17x - 6 = 0 => (3x-1) (x+6)
None of the answer equations have either of the same roots as the question equation...
So IMO "E" is correct answer... because none of the given answers share a common root of 3 (part of the solution) in any parts of their simplifications.
Answer: E
Question: In how many ways Chief Minister and Minister be elected from a team of 8 members?
Options:
A)124
B)29
C)32
D)56
E)65
Rationale: To do this, if captain is elected first, then we have 8 ways of doing this.
For election of vice-captain, we have only 7 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 8*7 = 56 ways.
D
Answer: D
Question: If -1 < h < 5, which of the following has the greatest value?
Options:
A)a) 1-h
B)b) 1+h
C)c) 1+h^2
D)d) 1-1/h
E)e) 1-1/(h^2)
Rationale: easiest way of solving this would be to substitute a value.
lets say h= - 1/2
a) 3/2
b) 1/2
c) 5/4
d) 3
e) - 3
the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.
Answer is E.
Answer: E
Question: How many words can be formed by using all letters of the word ‘DOHA’ ?
Options:
A)12
B)42
C)24
D)21
E)120
Rationale: Solution
The word DOHA contains 4 different letters.
Required number of words = 4P4 = 4 ! = (4 x 3 x 2 x 1) = 24
Answer C
Answer: C
Question: Find the odd man out
32, 34, 42, 46, 58, 59, 60, 66
Options:
A)31
B)41
C)67
D)59
E)61
Rationale: as 59 is only odd number.
ANSWER:D
Answer: D
Question: 40% of a number is added to 60, the result is the same number. Find the number?
Options:
A)300
B)288
C)270
D)100
E)281
Rationale: (40/100) * X + 60 = X
4x+600 = 10x
6x=600
x= 100
Answer : D
Answer: D
Question: If a2 + b2 + c2 = 560 and ab + bc + ca =8, then a + b + c is
Options:
A)4
B)52
C)16
D)24
E)64
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 560 and ab + bc + ca = 8,
(a + b + c)^2 = 560 + 2(8)
= 576
= 24^2
therefore: a + b + c = 24
ANSWER:D
Answer: D
Question: A can do a piece of work in 40 days; B can do the same in 20 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)24 days
B)65 days
C)86 days
D)40 days
E)17 days
Rationale: 10/40 + 10/20 + 10/x = 1
x = 40 days
Answer:D
Answer: D
Question: The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
Options:
A)4/7
B)3/2
C)3/5
D)9/4
E)3/1
Rationale: Let the earnings of P and Q be 9x and 10x respectively.
New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2
Answer: B
Answer: B
Question: X and Y are both integers. If X/Y = 50.60, then what is the sum of all the possible two digit remainders of X/Y?
Options:
A)315
B)616
C)672
D)900
E)1024
Rationale: Remainder = 0.60 --> 60/100 --> Can be written as (60/4) / (100/4) = 15/25
So remainders can be 15, 30, 45, 60, ..... 90.
We need the sum of only 2 digit remainders --> 15 + 30 + 45 + 60 + 75 + 90 = 315
Answer: A
Answer: A
Question: 1/2+[(2/11*11/32)+1]-9/16=
Options:
A)29/16
B)19/16
C)15/16
D)9/13
E)0
Rationale: 1/2 - [(2/11*11/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: E
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 850 in 4 years. The sum is?
Options:
A)s. 738
B)s. 750
C)s. 650
D)s. 730
E)s. 735
Rationale: S.I. for 1 year = (850 - 825) = Rs. 25
S.I. for 3 years = 25 * 3 = Rs. 75
Principal = (825 - 75) = Rs. 750.
ANSWER:B
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 59?
Options:
A)3944
B)920
C)7290
D)6928
E)4012
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 59 = Rs. 4012.
Answer: Option E
Answer: E
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7560 km and comes back to the starting point. The total time taken by him is:
Options:
A)914.2 hours
B)900 hours
C)915 hours
D)905 hours
E)960 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7560/18 + 7560/14 = 420 + 540 = 960 hours
Answer: Option E
Answer: E
Question: Solve the following quadratic equation by factoring.
U2-5U-14=0
Options:
A)-2,-7
B)2,-7
C)1,8
D)1,-8
E)2,6
Rationale: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(U+2)(U-7) = 0
U=-2 AND U = 7
ANSWER A
Answer: A
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
Options:
A)7
B)8
C)9
D)10
E)12
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: B
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 sec. The speed of the train is?
Options:
A)58 km/hr
B)50 km/hr
C)60 km/hr
D)98 km/hr
E)76
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 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
Question: Moli buys 3 ribbons,7 clips and 1 soap for Rs.120 exactly. At the same place it would cost Rs.164 for 4 ribbons, 10 clips and one soap. How much would it cost for one ribbon, one clip and one soap ?
Options:
A)36
B)34
C)38
D)32
E)31
Rationale: Explanation :
Let us consider, Ribbon is denoted by r
Clips is denoted by c
Soaps is denoted by s
Now according to the question,
=> 3r+7c+s = 120 -------- (1)
=> 4r+10c+s = 164 -------- (2)
(1) - (2)
=> (3r-4r) + (7c - 10c) +(s - s) = 120 - 164
=> -r - 3c = - 44
Multily the equation by -1 , it becomes
=> r + 3c = 44 ------- (3)
Now Perform this operation 2 * (1) - (2)
=> 2r+4c+s=76 ------- (4)
Finaly (4) - (3)
=> r + c + s=32
Hence, the cost of 1 ribbon ,1 clip and 1 saop would be 32 rs.
Answer : D
Answer: D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
Options:
A)17/29
B)17/21
C)17/22
D)17/20
E)17/34
Rationale: Explanation:
n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(Eá´œP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: D
Question: three friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $650. If one of the friends had a coupon for 35% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
Options:
A)$190
B)$141
C)$145
D)$137
E)$135
Rationale: 650 * 0,35 = 227
650 - 227 = 423
423 / 3= 141
Answer B
Answer: B