divelab/Sys2Bench huggingface dataset:
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 6
II. 12
III. 24
Options:
A)I, II, and III
B)I and II only
C)II and III only
D)I and III only
E)II only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: A
Question: A 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
Options:
A)260m
B)220m
C)230m
D)240m
E)250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+240/9=500/9
x=260
Ans is 260m
ANSWER: A
Answer: A
Question: A rower can row upstream at 7 km/hr and downstream at 15 km/hr. What is the rower's rate in still water?
Options:
A)9 km/hr
B)10 km/hr
C)11 km/hr
D)12 km/hr
E)13 km/hr
Rationale: The rate in still water is 1/2 * (15 + 7) = 11 km/hr
The answer is C.
Answer: C
Question: If W is the set of all the integers between 49 and 88, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Options:
A)11
B)44
C)48
D)28
E)26
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 87, the smallest is 51): 87 - 51 = 36
Step 2. Divide by 3: 36 / 3 = 12
Step 3. Add 1: 12 + 1 = 13.
So there are 13 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 88, the smallest is 50): 88 - 50 = 38
Step 2. Divide by 2: 38 / 2 = 19
Step 3. Add 1: 19 + 1 = 20.
So there are 19 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 13 multiples of 3 and the 19 multiples of 2: 13+19=32.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 13+19=32. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 32:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 84 - 54 = 30
Step 2. Divide by 6: 30 / 6 = 5
Step 3. Add 1: 5 + 1 = 6.
So there are 6 multiples of 6 within the range: we counted 6 numbers twice.
Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:
=13+19 - 6
= 32 - 6
= 26
Therefore, the final number of multiples of 2, 3 or 6 is 26.
Hence, this is the correct answer. (E)
Answer: E
Question: Two vertical pole of 2 m and 8 m stand apart on a horizontal plane.The height in meters at the point of intersection of the line joining the top of each pole to the bottom of other pole is ....
Options:
A)1.8
B)1.6
C)1.4
D)5.4
E)cannot be determined without knowing the distance bw the bottom of the pole
Rationale: formula is...(p*q)/p+q
here p=2,q=8
height in meters=(8*2)/8+2=16/10=1.6
ANSWER:C
Answer: C
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)11
B)61
C)88
D)66
E)35
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E
Answer: E
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 760 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
Options:
A)191
B)190
C)193
D)212
E)213
Rationale: Total movies submitted are 760.
As per question we need to take 1/4 of 760 to be considered for top 10 movies = 190
approximate the value we 190.
IMO option B is the correct answer...
Answer: B
Question: If 4 people are selected from a group of 8 married couples, what is the probability that none of them would be married to each other?
Options:
A)1/33
B)2/33
C)8/13
D)16/33
E)11/12
Rationale: If we are to select 4 people from 8 couples WITHOUT any restriction, how many ways can we make the selection? 16!/4!12! = 1820
If we are to select 4 people from 8 couples WITH restriction that no married couple can both make it to the group, only a representative?
8!/4!4! = 70
But we know that to select a person from each couple, take 2 possibilities
70*2*2*2*2 = 1120
Probability = Desired/All Possibilities = 1120/1820 = 8/13
Answer: C
Answer: C
Question: The cost of 3 chairs and 10 tables is Rs 9856. What is the cost of 6 chairs and 20
tables?
Options:
A)Rs 17227
B)Rs 18712
C)Rs 19172
D)Rs 19712
E)None
Rationale: Let the cost of one chair be Rs x and that of a table be = Rs y
According to the question,
3x + 10y = Rs 9856
⇒ 2 × (3x + 10y) = 2 × 9856
∴ 6x + 20y = Rs 19712
Answer D
Answer: D
Question: A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 7 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?
Options:
A)2:53 pm
B)3:03 pm
C)3:13 pm
D)3:23 pm
E)3:33 pm
Rationale: The question is asking when the first clock will have chirped 21 times (3*7 chirps).
The first clock chirps once every 3 minutes.
If the first chirp is at 2:03, then the 21st chirp is at 63 minutes after 2:00.
The answer is B.
Answer: B
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
Options:
A)10
B)100
C)1000
D)10000
E)100000
Rationale: Number of cubes=(100x100x100)/(10x10x10)=1000 Answer: C) 1000
Answer: C
Question: Which greatest possible length can be used to measure exactly 10 meter 40 cm, 14 meter 10 cm and 7 meter 90 cm
Options:
A)45cm
B)25cm
C)24cm
D)15cm
E)10cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1040 cm, 1410cm, 790cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 10.
Option E
Answer: E
Question: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?
Options:
A)Four
B)Five
C)Seven
D)Eight
E)Sixteen
Rationale: The number of ways of selecting 0 or more from n elements is 2^n.
Hence here, once you select w , the number of ways of selecting 0 or more from x,y and z ( 3 elements) is 2^3 = 8.
The same applies for {w, x, y}. If you select w here, the number of ways of selecting 0 or more from x and y = 2^2 = 4
ANSWER:A
Answer: A
Question: The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 6!?
Options:
A)3(5!)
B)5(5!)
C)4(5!)
D)6(5!)
E)7(5!)
Rationale: GCF is the product of common factors of the numbers involved.
GCF = 5!
a = 6! = 6*5!
b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)
Looking at the answers only 5 (5!) and 6! will have GCF as 5!
Ans B
Answer: B
Question: There are twelve consecutive flags at an equal interval of distance. A man passes the 8th flag in 8 seconds. How many more seconds will he take to pass the remaining 4 flags ?
Options:
A)2.57 seconds
B)3.57 seconds
C)4.57 seconds
D)5.57 seconds
E)6.57 seconds
Rationale: let the 1st flag i placed at the origin and the remaining on the X-axis.......then the coordinate on 8th flag is (7,0)..therefore distance travelled is 7 units in 4 second ......and coordinate of 12th flag is (11,0)..there r 4 units ....so time taken is (8*4)/7=4.57 seconds
ANSWER:C
Answer: C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)125/129
B)125/122
C)125/126
D)125/128
E)125/112
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer: C
Answer: C
Question: If a number is exactly divisible by 11 and 13, which of the following types the number must be?
Options:
A)Divisible by (11 + 13)
B)Divisible by (13 - 11)
C)Divisible by (11 x 13)
D)Divisible by (13 ÷ 11)
E)None
Rationale: Answer
LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13).
Correct Option: C
Answer: C
Question: A dance delegation of 4 people must be chosen from 5 pairs of dance partners. If 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
Options:
A)20
B)30
C)60
D)70
E)80
Rationale: Since 2 dance partners can never be together, lets select 4 pairs from 5 pairs of dance partners to fill the 4 positions. Now, in each position, each pair can be selected in 2 different ways.
Therefore number of ways of forming a delegation such that the 2 dance partners are never together = 5C4*(2C1)^4 = 5 * 16 = 80
Answer: E
Answer: E
Question: If x = 1- 2t and y = 2t - 2, then for what value of t does x = y?
Options:
A) 5/2
B) 3/2
C) 3/4
D) 2/5
E) 0
Rationale: We are given x = 1 – 2t and y = 2t – 2, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 2t for x and 2t – 2 for y in the equation x = y. This gives us:
1 – 2t = 2t – 2
3 = 4t
3/4 = t
The answer is C.
Answer: C
Question: If x and y are positive integers, and 4x^2=2y, then which of the following must be a multiple of 9?
I. x^2
II. y^2
III. xy
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II and III
Rationale: 4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is B
Answer: B
Question: The average (arithmetic mean) of 20, 40, and 60 is 8 more than the average of 10, 70, and what number?
Options:
A)16
B)25
C)35
D)45
E)55
Rationale: a1 = 120/3 = 40
a2 = a1 -8 = 32
sum of second list = 32*3 = 96
therefore the number = 96 -80 = 16
ANSWER:A
Answer: A
Question: Anil had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product?
Options:
A)1590
B)1600
C)1950
D)1630
E)1760
Rationale: Explanation :
Let the number that Anil wanted to multiply be 'Y'.
He was expected to find the value of 35Y.
Instead, he found the value of 53Y.
The difference between the value that he got (53Y) and what he was expected to get (35Y) is 540.
=> 53Y - 35Y = 540
=> (53 - 35) * Y = 540
=> Y = 30
Therefore, the correct product = 53 * 30 = 1590
Answer : A
Answer: A
Question: Murali travelled from city A to city B at a speed of 50 kmph and from city B to city C at 50 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?
Options:
A)kmph
B)kmph
C)kmph
D)kmph
E)kmph
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)/50 + (3x)/50
= (2x + 3x)/50 = 5x/100
= x/20 Average speed
= (2x + 3x)/(x/20) = 100 kmph.
Answer: B
Answer: B
Question: A city council will select 2 of 9 available firefighters and 1 of 4 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
Options:
A)36
B)72
C)144
D)216
E)432
Rationale: OA D
9C2 * 4C1
using the combination formula to choose 2 from 9 and 1 from 4
C
Answer: C
Question: you need to pict any number from 1, 3,5,7,9,11,13 and 15 to make below equation true.
()+()+()=30
can you solve it?
Options:
A)7+15+9
B)6+15+9
C)6+14+9
D)6+15+8
E)8+15+9
Rationale: Correct Answer : B
3x+15+9=30
3x =3*2*1 =6
therefore :- 6+15+9= 30
Answer: B
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum Z of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
Options:
A) 5
B) 7
C) 9
D) 10
E) 14
Rationale: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum Z of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D
Answer: D
Question: If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission?
Options:
A)4%
B)0.4%
C)0.04%
D)0.004%
E)0.0004%
Rationale: % of sales amount of commission
= (Commission/Total Value) *100
= (0.8/2000) * 100
= 0.04%
The answer is C.
Answer: C
Question: A bookseller sells his books at a 10% markup in price. If he sells a book for $11.00, how much did he pay for it?
Options:
A)$14.40
B)$14.00
C)$10.00
D)$9.60
E)$5.00
Rationale: Let the cost price of book = x
Selling price of book = 11$
Markup % = 10
(110/100)x = 11
=> x = 10
Answer C
Answer: C
Question: Which of the following could be the sides of an obtuse angled triangle? all values are in degree
I. 19, 29, 39
II. 29, 39, 49
III. 10,110, 60
Options:
A)III only
B)II only
C)III only
D)I and II only
E)I, II and III
Rationale: obtuse angled triangle means one angle more than 90deg and total 180 deg.. III
A
Answer: A
Question: With what number must 6.2587 be multiplied in order to obtain the number 625.87?
Options:
A)1000
B)1,0000
C)100
D)100,000
E)None of these
Rationale: Explanation: The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.
Answer : (C)
Answer: C
Question: Students of three different classes appeared in common examination. Pass average of 10 students of first class was 60%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
Options:
A)74%
B)75%
C)69%
D)70%
E)None
Rationale: Solution:
Sum of pass students of first, second and third class,
= (60% of 10) + (60% of 15)+ (80% of 25)
= 6+9+20 = 35
Total students appeared,
= 10+15+25 = 50
Pass average,
= 35*100/50 = 70%.
Answer: Option D
Answer: D
Question: A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
Options:
A)7 km/hr
B)7.2 km/hr
C)7.4 km/hr
D)7.8 km/hr
E)8.9 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: B
Question: Which of the following inequalities is always true for any non-negative real numbers numbers 'x' and 'y'?
Options:
A)(x-y)^2 >= x^2 + y^2
B)(x+y)^2 <= x^2 + y^2
C)(x+y)^2 = x^2 + y^2
D)(x+y)^2 <= x^2 + y^2
E)(x+y)^2 >= x^2 + y^2
Rationale: Using the concept of superadditivity, we know that for non-negative real numbers the square of the sum of x and y will always be more than the sums of x and y separately; this is a superadditive function. Therefore the answer is E.
Answer: E
Question: In a certain sequence, the first term is 2, and each successive term is 2 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
Options:
A)13/8
B)21/13
C)58/5
D)70/29
E)82/13
Rationale: let five terms in the sequence be a,b,c,d,e
a=2
b= 2+1/2=5/2
c=2+2/5= 12/5
d= 2+5/12 = 29/12
e= 2+12/29 = 70/29
hence answer should be D.
Answer: D
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Total Distance = 74 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 70 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 70 / 10 = 7 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 7 = 28+4 = 32 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 32 /4 = 8 hrs ... Answer E
Answer: E
Question: The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Explanation :
Let α is the common root.
∴ α3 + 3α2 + 4α + 5 = 0. ............................(i)
α3 + 2α2 + 7α + 3 = 0. .............................(ii)
On subtracting (ii) from (i), we get
α2 - 3α + 2 = 0.
α = 2, α = 1.
But the above values of α do not satisfy any of the equations. Thus, no root is common.
Answer : A
Answer: A
Question: If 4XZ + YW = 4 and XW + YZ = 8, what is the value of the expression (2X + Y)(2Z + W)?
Options:
A)22
B)20
C)24
D)26
E)28
Rationale: (2x+y)*(2z+w) = 4+2(8) =20
Answer : B
Answer: B
Question: B completes a work in 7 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
Options:
A)3.75 days
B)4.11 days
C)5.11days
D)6.75 days
E)7.33 days
Rationale: 1/7 + 1/10 = 17/70
70/17 = 4.11 days
ANSWER:B
Answer: B
Question: In one hour, a boat goes 8 km along the stream and 2 km against the stream. the sped of the boat in still water (in km/hr) is :
Options:
A)3
B)5
C)8
D)9
E)10
Rationale: Solution
Speed in still water= 1/2(8+2) km/hr= 5kmph. Answer B
Answer: B
Question: If x/4 + 24/x = 5, what are the values of 2x - 7?
Options:
A)8 and 9
B)8 and 24
C)17 and 21
D)12 and 29
E)17 and 9
Rationale: I got the same thing E is the answer 9 or 17
Answer: E
Question: There are three departments having students 62,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
Options:
A)72
B)74
C)75
D)76
E)77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 62/2 = 31
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 31+12+29 = 72
ANSWER:A
Answer: A
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 350 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Options:
A)237
B)287
C)197
D)287
E)700
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 350) = 2 + 2(extra)
=> 2x - 700 = x => x = 700.
Answer: E
Answer: E
Question: P runs 25% faster than Q so P gives Q a 60 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
Options:
A)100
B)200
C)300
D)400
E)500
Rationale: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.25V = (D-60) / V
D=1.25D-75
0.25D=75
D=300 meters.
The answer is C.
Answer: C
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64500. What is his profit percent?
Options:
A)22
B)77
C)17.3
D)99
E)88
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64500
Profit(%) = (64500 - 55000)/55000 * 100 = 17.3%
Answer: C
Answer: C
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)5
B)2
C)9
D)5
E)1
Rationale: 1250
= D(100/4)2
D = 2
Answer: B
Answer: B
Question: Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: For: (2^(3x+3)+3)/3
Let n = 3x + 3
2^n
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....
Rule: x^(m+n) = (x^m)(x^n)
(2^(3x))(2^3)
Rule: x^(mn) = (x^m)^n
((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.
Answer: B
Answer: B
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party W. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
Options:
A)15
B)20
C)30
D)35
E)45
Rationale: S=100
not( W and B ) =35
only W=20
(W and B)/B=1/2
let ( W and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: A
Question: If x < y < z and y-x > 11, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
Options:
A)6
B)7
C)8
D)9
E)15
Rationale: We have:
1) x<y<z
2) y-x>11
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>11, the least value for y-x must be 13, the least value for x must be 2, and, thus, the least possible value for y must be 15 (y-2=13, y=15)
2<15<z, since z is odd, the least possible value for z is 17
z-x=17-2=15
Answer E
Answer: E
Question: The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 22. What is the cost price of the article?
Options:
A)Rs. 40
B)Rs. 50
C)Rs. 49
D)Rs. 59
E)Rs.44
Rationale: S.P 1- C.P = C.P – S.P 2
66 - C.P = C.P - 22
2 C.P = 66 + 22;
C.P = 88/2 = 44
ANSWER:E
Answer: E
Question: If 25% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
Options:
A)4:3
B)1:4
C)3:7
D)6:11
E)2:3
Rationale: Let 25% of A = 1/3 B
then 25A/100 = 1B/3
A/4 = B/3
A/B = 4/3
A:B = 4:3
Answer is A
Answer: A
Question: If 7a - 3b = 10b + 50 = -12b - 2a, what is the value of 9a + 9b?
Options:
A)-9
B)-6
C)0
D)6
E)9
Rationale: (i) 7a - 13b = 50
(ii) 2a + 22b = -50
Adding (i) and (ii):
9a + 9b = 0
The answer is C.
Answer: C
Question: A pupil's marks were wrongly entered as 73 instead of 40. Due to the average marks for the class got increased by half. The number of pupils in the class is?
Options:
A)18
B)82
C)66
D)27
E)77
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (73 - 40) => x/2
= 33 => x = 66.
Answer: C
Answer: C