CAT 2019 Quant Question: Linear & quadratic equations
The quadratic equation 
+ bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of 
+ c?
A. 3721
B. 549
C. 361
D. 427
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Answer:
Given quadratic equation is 
Sum of roots = -b
-b = 4a + 3a
-b = 7a
Product of the roots = c
c = 4a x 3a
Our answer must be a multiple of 61, which should be a perfect square
Going through the options,
549 = 61 x 9
Thus, possible value of 
Hence, the answer is 549
Choice B is the correct answer.
CAT 2019 Quant Question: Number theory
In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is [TITA]
Answer:
Let the first digit be = a
Second digit = Twice of first digit = 2a
Third digit = First digit = a
Fifth digit = Sum of first two digits = a + 2a = 3a
Sixth digit = Sum of first three digits = a + 2a + a = 4a
Fourth digit = Sum of fifth and sixth digit = 3a + 4a = 7a
Largest possible value of fourth digit = 7 (any more than that would be > 10 and not satisfy the condition)
Hence, the answer is 7
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CAT 2019 Quant Question: Profit & loss
Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was
A. 2000
B. 6000
C. 8000
D. 4000
Answer:
Let the cost price of one bicycle = Rs. x
Total cost price = Rs. 10x
He made a total profit of 25% on 6 cycles and 25% loss on 4 cycles and made a profit of Rs. 2000
So, 2000 = 6 x 
- 4 x
2000 = 
x = Rs. 4000
Hence, the answer is 4000
Choice D is the correct answer.
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CAT 2019 Quant Question: Sequence & series
The number of common terms in the two sequences: 15, 19, 23, 27, … , 415 and 14, 19, 24, 29, … , 464 is
A. 20
B. 18
C. 21
D. 19
Answer:
First series - 15, 19, 23, 27, …, 415 → Common difference = 4
Second series - 14, 19, 24, 29, …, 464 → Common difference = 5
Common terms in both sequences = 19, 39, 59, …, (Common difference = LCM (4,5) = 20)
Now, observing the new series
19, 39, 59, …, = (20 - 1), (40 -1), (60 -1), …, (400-1) (There is no room for 419, as the first series ends at 415)
399 = 400 - 1 = 20 x 20 -1
Hence, the number of common terms in the two sequences = 20
Hence, the answer is 20
Choice A is the correct answer.
CAT 2019 Quant Question: Sequence & series
If (2n+1) + (2n+3) + (2n+5) + … + (2n+47) = 5280 , then what is the value of 1+2+3+ … +n ? [TITA]
Answer:
Given series - (2n+1) + (2n+3) + (2n+5) + … + (2n+47) = 5280
Isolate 2n terms on one side
(2n + 2n +… + 2n) + (1 +3 + 5 +… + 47) = 5280
Odd numbers from 1 to 47 are added in the above series.
Number of terms from 1 to 47 = 24 terms
Therefore, the number of 2n terms = 24
For computing the value of (1 +3 + 5 +… + 47),
2n = 220 - 24
n = 110 - 12
n = 98
So, value of 1+2+3+…+98 = 
= 
= 
Value of 1+2+3+…+98 = 4851
Hence, the answer is 4851
CAT 2019 Quant Question: Mixtures
The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is
A. 15
B. 12
C. 13
D. 14
Answer:
Vessels A, B and C contains salt solution of strengths 10%, 22% and 32% respectively
It is also given that the amount of salt solution = 500 ml
So, Vessels A, B and C contains salt of 50 grams, 110 grams and 160 grams respectively
100 ml of Solution is transferred from A to B:
A would have 400 ml, B would have 600 ml of solution
Amount salt from A which is transferred to B = 
= 10 grams
So, Total salt in B = 110 + 10 = 120 grams (After first transfer)
Total salt in A = 40 grams (After first transfer)
Now, 100 ml from Vessel B is transferred to Vessel C
So similarly, 
of salt would transfer from B to C
Total Salt in B = 120 - 20 = 100 grams (After second transfer)
Total Salt in C = 160 + 20 = 180 grams (After second transfer)
Now, 100 ml from Vessel C is transferred to Vessel A
So similarly, of salt would transfer from C to A
Total Salt in C = 160 - 30 = 130 grams (After third transfer)
Total Salt in A = 40 + 30 = 70 grams (After third transfer)
So, Vessel A contains 70 grams Salt in 500 ml solution
Strength of Salt Solution in Vessel A = 14%
Choice D is the correct answer.
CAT 2019 Quant Question: Exponents & Powers
Answer:
So, 5k - m = 13538 ---- (1)
k + 3m = 9686 ---- (2)
Multiply (1) by 3,
15k - 3m = 40314 ----(3)
Adding (2) and (3) we get,
16k = 50000
k = 625 x 5
So, x - 1 = 5
x = 6
We know, k + 3m = 9686
3125 + 3m = 9686
3m = 6561
m = 2187
y = 7
x + y = 6 + 7 = 13
Hence, the answer is 13
CAT 2019 Quant Question: Simple interest & Compound interest
Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is [TITA]
Answer:
The amount on the first investment of Anmol = 12,000 * (1.08) = 12,960
So the Interest on this investment is 12,960 - 12,000 = 960.
The amount on the second investment of Anmol = 10,000 * (1.03)2 = 10,609
So the Interest on this investment is 10,609 - 10,000 = 609.
So the total interest on these returns = 960 + 609 = 1,569.
Bimal has to get this as Simple Interest by investing X rupees at 7.5%
That means, X * 0.075 = 1,569
X = 20,920
So, Bimal has to invest 20,920 rupees.
Hence, the answer is 20920
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CAT 2019 Quant Question: Profit & loss
A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x - y) / p equals
A. 1
B. 1.2
C. 0.7
D. 0.50