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CAT workshop- Algebra- Part 1
Question: Total integer pair(s) (x, y) satisfying the equation x + y = xy is/are
1) 0
2) 1
3) 2
4) 3
Question: How many positive integer pairs (a, b) satisfy the equation ab = a + b + 20?
A
...
2
C
...
4
Question: In a broken calculator, the keys '+' and '×' have their functions switched
...
0
B
...
2
D
...
A
...
2
B
...
5
C
...
2
D
...
2
Question: When the sum of two natural numbers is multiplied by each number separately,
the products obtained are 2418 and 3666
...
16
2
...
26
4
...
(a) 0
(b) 3
(c) 2
(d) 1
Question: If the polynomial ax4 + bx3 + cx2 + dx + e has the property that the product of its
roots is 1/3rd of the sum taking two roots at a time, then find the relationship between e
and c
...
A
...
394
C
...
432
Question: Find the nature of roots of the following equations:
(i) x2 + 9x + 27 = 0
(ii) 6x2 - 13x - 5 = 0
A
...
(i) Real (ii) Imaginary
(i) Imaginary (ii) Imaginary
C
...
Question: The roots of x3 − ax2 + bx − c = 0 are p, q and r, while the roots of x3 + dx2 + ex −
80 = 0 are p + 4, q + 4 and r + 4
...
32
B
...
216
D
...
25,000, are to be divided into two
groups, such that one-fourth of the number of diamonds in the first group would be 20
more than one-sixth of the number of diamonds in the second group
...
If each teacher had been older by 1 year, each doctor by 6
years and each lawyer by 7 years, their average age would have increased by 5 years
...
Michael Swrfieai went to purchase a certain number of
balls
...
A leather
ball was 70 cents costlier than a tennis ball
...
60 cents
2
...
80 cents
4
...
6
B
...
8
D
...
A said to B, ''If you give me one of your
stamps, we shall have equal number of stamps''
...
Find the total number of stamps
with A and B
...
A student scores 1 mark for a correct answer, –1/3 for a
wrong answer and –1/6 for not attempting a question
...
Your daughter is one-sixth the age of my great-grandfather
...
" Banke Lal replied, "My second wife is older than your
only wife by one-seventh
...
'' What would have been
the age of Ghosh Babu's great-grandfather at the time of this conversation?
A
...
100 years
C
...
90 years
Question: 36 coins are divided among A, B, C and D, such that B takes more than A, C takes
more than B and D takes more than C
...
The first dealer purchased 1 Airedale, 3
Spaniels and 7 puppies and paid $1400; and the second purchased 1 Airedale, 4 Spaniels
and 10 puppies and paid $1700
...
How much did
the third and fourth dealers pay, separately?
(a) $9500; $800 (b) $9500; $1000 (c) $8600; $8100 (d) $7500; $2500
Question: At an entrance test for a business course, the students score 1 mark for every
right answer and lose 1/4 mark for every wrong answer
...
To gain admission, a student has to score 60 or above
...
After the test he realised that to gain
admission, not more than 20 of his answered questions should be wrong
...
How many questions did he leave
unanswered?
Question: Three drunkards agreed to pool their vodka and decided to share it with the
fourth drunkard (who had no vodka) at a price equal to 5 roubles a litre
...
Then, all four of them divided the vodka equally and drank it
...
It was found that the first drunkard got twice as much money as the second
...
10
B
...
5
D