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26 Jan 2022, 06:00
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Difficulty:
35%
(medium)
Question Stats:
71% (02:00) correct
29%
(02:37)
wrong
based on 42
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What is the remainder when the positive three-digit number 1yz is divided by 7?
(1) y + z = 7
(2) y -2 is a non-zero positive number divisible by 3
(1) y + z = 7
(2) y -2 is a non-zero positive number divisible by 3
29 Jan 2022, 02:42
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1yz is a positive three-digit number. So,
0<= y,z<=9
(1) y + z = 7
If y = 1 and z = 6 then 1yz = 116. Number 116 divided by 7, remainder is 4.
If y = 6 and z = 1 then 1yz = 161. Number 161 is divisible by 7, so remainder is 0.
Using statement 1 alone, we have different answer to the Data sufficiency question. Hence, statement 1 alone is insufficient.
(2) y -2 is a non-zero positive number divisible by 3
=> y-2 = 3, 6, 9, ...
=> y = 5, 8, 11, ...
But, because y is a single digit number y = 5, 8
If y=5 and z=4 then 1yz = 154 which is divisible by 7, so remainder is 0.
If y=5 and z=3 then 1yz = 153 which is not divisible by 7, so remainder is 6..
Using statement 2 alone, we have different answer to the Data sufficiency question. Hence, statement 2 alone is insufficient.
Combining 1 and 2 we have,
y=5 or 8 and y+z=7
But because y and z are +ve, y cannot be 8.
=> y = 5 and z = 2.
Number 1yz = 152, which when divided by 7 remainder is 5. Combining statements 1 and 2 we get a definite answer.
Hence, statements 1 and 2 together are sufficient.
Answer C.
0<= y,z<=9
(1) y + z = 7
If y = 1 and z = 6 then 1yz = 116. Number 116 divided by 7, remainder is 4.
If y = 6 and z = 1 then 1yz = 161. Number 161 is divisible by 7, so remainder is 0.
Using statement 1 alone, we have different answer to the Data sufficiency question. Hence, statement 1 alone is insufficient.
(2) y -2 is a non-zero positive number divisible by 3
=> y-2 = 3, 6, 9, ...
=> y = 5, 8, 11, ...
But, because y is a single digit number y = 5, 8
If y=5 and z=4 then 1yz = 154 which is divisible by 7, so remainder is 0.
If y=5 and z=3 then 1yz = 153 which is not divisible by 7, so remainder is 6..
Using statement 2 alone, we have different answer to the Data sufficiency question. Hence, statement 2 alone is insufficient.
Combining 1 and 2 we have,
y=5 or 8 and y+z=7
But because y and z are +ve, y cannot be 8.
=> y = 5 and z = 2.
Number 1yz = 152, which when divided by 7 remainder is 5. Combining statements 1 and 2 we get a definite answer.
Hence, statements 1 and 2 together are sufficient.
Answer C.
29 Jan 2022, 16:37
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(1) possibilities -
116 --> rem 4
125 --> rem 6
134 --> rem 1
143 --> rem 3
152 --> rem 5
161 --> rem 0
(2) not sufficient, can be 152 or 153, or 181 and so on....
(1)+(2) 152 is the only possibility
Answer: C
116 --> rem 4
125 --> rem 6
134 --> rem 1
143 --> rem 3
152 --> rem 5
161 --> rem 0
(2) not sufficient, can be 152 or 153, or 181 and so on....
(1)+(2) 152 is the only possibility
Answer: C
