允许两数重复的情况下
答案为x=1, y=4; 甲知道和A=x+y=5, 乙知道积B=x*y=4 不允许两数重复的情况下有两种答案
答案1: 为x=1, y=6; 甲知道和A=x+y=7, 乙知道积B=x*y=6 答案2: 为x=1, y=8; 甲知道和A=x+y=9, 乙知道积B=x*y=8
解：
设这两个数为x,y.
甲知道两数之和 A=x+y; 乙知道两数之积 B=x*y;
该题分两种情况
允许重复,有(1 <= x <= y <= 30); 不允许重复,有(1 <= x < y <= 30);
当不允许重复, 即(1 <= x < y <= 30);
1)由题设条件：乙不知道答案 <=> B=x*y 解不唯一 => B=x*y 为非质数
又∵ x ≠ y
∴ B ≠ k*k (其中k∈N)
结论(推论1)：
B=x*y 非质数且 B ≠ k*k (其中k∈N) 即：B ∈(6,8,10,12,14,15,18,20...) 证明过程略
2)由题设条件：甲不知道答案 <=> A=x+y 解不唯一 => A >= 5;
分两种情况
A=5,A=6时x,y有双解
A>=7 时x,y有三重及三重以上解
假设 A=x+y=5 则有双解
x1=1,y1=4; x2=2,y2=3
代入公式B=x*y:
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B1=x1*y1=1*4=4; (不满足推论1，舍去) B2=x2*y2=2*3=6;
得到唯一解x=2,y=3即甲知道答案 与题设条件：“甲不知道答案”相矛盾 故假设不成立， A=x+y≠5
假设 A=x+y=6 则有双解 x1=1,y1=5; x2=2,y2=4
代入公式B=x*y:
B1=x1*y1=1*5=5; (不满足推论1，舍去) B2=x2*y2=2*4=8; 得到唯一解x=2,y=4
即甲知道答案
与题设条件：“甲不知道答案”相矛盾 故假设不成立， A=x+y≠6
当A>=7时
∵ x,y的解至少存在两种满足推论1的解 B1=x1*y1=2*(A-2) B2=x2*y2=3*(A-3) ∴ 符合条件
结论(推论2)：A >= 7
3)由题设条件：乙说“那我知道了”
=> 乙通过已知条件B=x*y及推论(1)(2)可以得出唯一解 即：
A=x+y,A >= 7
B=x*y,B ∈(6,8,10,12,14,15,16,18,20...) 1 <= x < y <= 30 x,y存在唯一解
当 B=6 时：有两组解
x1=1, y1=6
x2=2, y2=3 (∵ x2+y2=2+3=5 < 7∴不合题意，舍去) 得到唯一解 x=1, y=6
当 B=8 时：有两组解
x1=1, y1=8
x2=2, y2=4 (∵ x2+y2=2+4=6 < 7∴不合题意，舍去) 得到唯一解 x=1, y=8
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当 B>8 时：容易证明均为多重解
结论：
当B=6时有唯一解 x=1, y=6当B=8时有唯一解 x=1, y=8
4)由题设条件：甲说“那我也知道了”
=> 甲通过已知条件A=x+y及推论(3)可以得出唯一解
综上所述，原题所求有两组解： x1=1, y1=6 x2=1, y2=8
当x<=y时，有(1 <= x <= y <= 30); 同理可得唯一解 x=1, y=4 Aptitude Paper : IBM
1. In 1978, a kg of paper was sold at Rs25/-. If the paper rate increases at 1.5% more than the inflation rate which is 6.5% a year, then what wil be the cost of a kg of paper after 2 years? (a) 29.12 (b) 29.72 ? 30.12 (d) 32.65
(e) none of these
2. In A,B,C are having some marbles with each of them.
A has given B and C the same number of marbles each of them already have. Then, B gave C and A the same number of marbles they already have. Then C gave A and B the same number of marbles they already have. At the end A,B,and C have equal number of marbles. (i) If x,y,z are the marbles initially with A,B,C respectively. Then the number of marbles B have at the end (a) 2(x-y-z) (b) 4(x-y-z) ? 2(3y-x-z) (d) x + y-z Ans. ?
(ii) If the total number of marbles are 72, then the number of marbles with A at the starting (a) 20 (b) 30 ? 32 (d) 39
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Ans. (d)
3. If a car starts from A towards B with some velocity.
Due to some problem in the engine after travelling 30km, the car goes with 4/5 th of its actual velocity The car reaches B 45 min later to the actual time.
If the car engine fails ofter travelling 45km, the car reaches the destination B 36min late to the actual time What is the initial velocity of car and what is the distance between A and B in km?
Ans. 20 & 130. 25 & 105
4. A person has Rs 100/- in his pocket, he can as 25 pencils or 15 books. He kept 15% of the money for travelling expenses and purchased 5 pencils. So how many books he can purchase with the remaining money.
5. Ten questions on analogies. eg: chief : tribe :: governer : state epaulette : shoulder :: tiara : head guttural : throat :: gastric : stomach inept : clever :: languid : active knife : butcher :: hammer : carpenter ::
7. In a computer institute 9 languages can be taught.
The module is of 6 months duration and of the six languages only one can be taught each month .
In addition to that BASIC is always taught and should be in first month itself WORD PERFECT is to be taught in the preceeding week of WORD STAR.
FORTRAN can not be taught until COBAL is taught prior to that BINO, FIFO can never be taught in single module
languages are BASIC, WORD STAR, WORD PERFECT, FORTRAN, COBAL, BINO, FIFO, LOTUS, C
i) If word star is in 3rd month , what could be in 6th month.
ii) If COBAL is in the 2nd month and BINO in 6th month. FORTRAN will betaught in which month.
8. In a class, except 18 all are above 50 years.
15 are below 50 years of age. How many people are there (a) 30 (b) 33 ? 36
(d) none of these.
Ans. (d)
9. A square plate of some size is cut at four corners. Equal squares of the
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same size are cut and is formed as open box.
If this open box carries 128 ml of oil. What is the size of the side of the plate? (a) 17 (b) 14 ? 13
(d) None of these
10. In a square, all the mid points are joined. The inner square is shaded. If the area of the square is A, what is the area of the shaded area?
11. Two questions on basic angles i.e given a circle, a few chords or diameter is drawn etc.
12. If the follwoing statements are given @(a,b)= (a+b)/2 /(a,b)= a/b *(a,b)= ab
If a=1, b=2 then find i) /(a,(@(a,b),*(a,b))) ii) */(a,@(*(a,b)))
13. If the follwoing statements are given
(x#y) = x + y- xy (x*y) = (x + y)/2
i) Find the values of x, y will satisfy this equation (x#y)#(x*y) < (x#y) ii) Find the values of x, y will satisfy this equation (a*b)#(b*c)< (a#b)*(b*c)
-------------------------------------------------------------------- Quantitative Paper : IBM Global Servicesl
1.A clerk multiplied a number by ten when it should have been divided by ten.The ans he got was 100.what should the ans have been? a:1
2.If Rs20/- is available to pay for typing a research report & typist A produces 42 pages and typist B produces 28 pages.How much should typist A receive? a:Rs12/-
3.The average salary of 3 workers is 95 Rs. per week. If one earns Rs.115 and second earns Rs.65 how much is the salary of the 3rd worker. Ans.105.
4.A 16 stored building has 12000 sq.feet on each floor. Company A rents 7 floors and company B rents 4 floors. What is the number of sq.feet of unrented floor space.
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