Around the World in 80 Questions (Day 8): If d is a single-digit numb

Answer A
Statement one alone is sufficient where we get 3 as a possible value
But in statement 2 we get 2 values 3 and 9.

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My Answer: E, both statements together are not sufficient.

For both statements, d could be either 3 or 9. Hence, both statements together are also insufficient.

Asked: If d is a single-digit number greater than 1, what is the value of d ?

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
Since d is a factor of the two digit number d3, d3 is NOT a prime number
Non- prime numbers d3 = {33, 63, 93} = {3*11, 3*3*7, 3*31}
d3 = 33; Since d is factor of two digit number d3.
d = 3
SUFFICIENT

(1) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
Since d is a factor of the two digit number d9, d9 is NOT a prime number
Non- prime numbers d9 = {39, 49, 69, 99} = {3*13, 7*7, 3*23, 3*3*11}
d9 = {39,99}; Since d is factor of two digit number d9.
d = {3, 9}
NOT SUFFICIENT

IMO A

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.

10d + 3 = d.p, where p is an integer.
d must be 3 because 10d and 3 must have atleast one common factor other than 1.
1 is sufficient.

(2) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
10d + 9 = d.p, where p is an integer.
d can be 3 or 9 because 10d and 9 must have atleast one common factor other than 1.
So, 2 is insufficient.

A is the correct choice.

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
d can be 1 or 3 but given that d>1 hence this is sufficient

(1) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
d can be 1, 3 or 9. 3 and 9 are both >1 hence insufficient

Therefore answer is A

8 possible values of d = 2,3,4,5......,8,9

(1) 2 is not a factor of 23
3 is a factor of 33
4 is not a factor of 43
5 is not a factor of 53
6 is not a factor of 63
7 is not a factor of 73
8 is not a factor of 83
So d= 3---------SUFFICIENT

(2) 2 is not a factor of 29
3 is a factor of 39
4 is not a factor of 49
5 is not a factor of 59
6 is not a factor of 69
7 is not a factor of 79
8 is not a factor of 89
9 is a factor of 99

So d can be 3 or 9.-----------> NOT SUFFICIENT

OA: A

If d is a single-digit number greater than 1, what is the value of d ?

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.

List out all the possible answers: 23, 33, 43, 53, 63, 73, 83, 93 with d as the tenth digit. On number that is factorable is 33, which is 3 * 11. Sufficient

(2) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.

List out all the possible answers: 29,39,49,59,69,79,89,99. d as the tenth digit and factorable are 39, where 3*13, and 99, where 9*11. Not sufficient

Answer is (A)

Given :d is a single-digit number greater than 1

d can be 2,3,4,5,6,7,8,9

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
We can do trial and error since the total set of possible integers is small.
2 is NOT a factor of 23
3 IS a factor of 33
4 is NOT a factor of 43
5 is NOT a factor of 53
6 is NOT a factor of 63
7 is NOT a factor of 73
8 is NOT a factor of 83
9 is NOT a factor of 93

Since there is only one possible value of d ( i.e 3) this choice is Sufficient.

(2) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
We can do trial and error since the total set of possible integers is small.
2 is NOT a factor of 29
3 IS a factor of 39
4 is NOT a factor of 49
5 is NOT a factor of 59
6 is NOT a factor of 69
7 is NOT a factor of 79
8 is NOT a factor of 89
9 IS a factor of 99

Since there are two possible values of d ( 3 and 9) this choice is not Sufficient.

Answer : A

d is a single-digit and > 1 => d {2,3,4,5,6,7,8,9}
Q: what is d?

1) d is a factor of d3 (2-digit no.)
=> d cannot be even because d3 is not even; d can be 3,5,7, or 9
=> d3 is not divisible by 5; d can be 3,7, or 9
=> 73 is not divisible by 7 and 93 is not divisible by 9, but 33 is divisible by 3
=> d = 3 ---> SUFFICIENT

2) d is a factor of d9 (2-digit no.)
=> d cannot be even because d9 is not even; d can be 3,5,7, or 9
=> d3 is not divisible by 5; d can be 3,7, or 9
=> 79 is not divisible by 7, but 99 is divisible by 9 and 33 is divisible by 3
=> d = 3 or 9 ---> NOT SUFFICIENT

Answer = [A]

If d is a single-digit number greater than 1, what is the value of d ?
so d could be 2 to 9

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
suppose d3 is 33 hence 3 is a factor of 33
suppose d3 is 63 but 6 is not a factor of 63
if d3 is 93 ; 9 is not a factor of 93
hence we know that d = 3 --> only A and D left
(1) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
suppose d=3 hence 3 is a factor of 39
suppose d=9 hence 9 is a factor of 99
hence d can be 2 number ---> insufficient
The answer is A

statement 1
last digit is 3
so the factor of d3 can be 3, 7 ,9
if we take
d=3
no=33(satisfies condition)
d=7
no=73(not satisfies condition)
d=9
no=93(not satisfies condition)
so d=3
statement 1 is sufficient
statement 2
last digit is 9
factors of d9 can be 3,7,9
if
d=3
no=39(satisfies cond)
d=7
no=79(not satisfies cond)
d=9
no =99(satisfies cond )
d can be 3 ,9
we dont have single value of d
so 2 alone is not suff

IMO A

If d is a single-digit number greater than 1, what is the value of d ?

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
(1) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.

D = (2,3,4,5,6,7,8,9)
D = ?

Statement 1:

d3 and d is factor of d3

We can have 23,33,43,53,63,73,83,93

Only d = 3 satisfies this and hence SUFFICIENT.

Statement 2:

d9 and d is factor of d9

We can have 29,39,49,59,69,79,89,99

Both 3 and 9 can be factors. NOT SUFFICIENT

If d is a single-digit number greater than 1, what is the value of d ?

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
(1) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
______________________________________________________
So, D is equal to 1<d<10 as it is a single digit.
(1) d3 can be
13, 23, 33, 43, 53, 63, 73, 83,93.
1 can be a factor of 13
3 can be a factor of 33
We can only take only 3 with abovementioned requirement. - Sufficient

(2) d9 can be
19,29,39,49,59,69,79,89,99
1 can be a factor of 19
3 can be a factor of 33
9 can be a factor of 99
we can take 3 and 9. Since, both numbers are greater than 1. - Insufficient

A is our winner.
Hope it helps .

In statement (1), the possible cases are(23,33,43,53,63,73,83,93). We need to see which of these numbers are divisible by their unit digits. Only one number, 33, qualifies. Hence d=3. Sufficient.
In statement (2), the possible cases are(29,39,49,59,69,79,89,99). We again need to see which of these numbers are divisible by their unit digits. Two numbers, 39 and 99 qualify. Hence d could be 3 or 9. Insuffcient.
A is the answer.

From given information d can be 2 to 9

Statement a gives 10d+3. Now d has to be factor
Putting values of d from 2 to 9 we get single value of d as 3

Statement a is sufficient

Statement b gives 10d+9 now putting value of d it comes that 2 such nos are possible 39 and 99 giving value of d as 3 and 9 so not sufficient

Hence a is correct answer

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From the Question Stem,
The possible values of d are : {2,3,4,5,6,7,8 and 9}

Statement 1:
The only value of d that satisfies this is d = 3 ( i.e. 3 is a factor of 33) since no other value of d satisfies this condition.
Hence, sufficient

Statement 2:
This can be satisfied when d = 3 or d =9 (i.e. 3 is a factor of 39 and 9 is a factor of 99).
Hence not sufficient

Therefore the answer is option A

If d is a single-digit number greater than 1, what is the value of d ?

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
(2) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.

Solution:
Given, 2=<d=<9.

(1) d is a factor of the two digit number d3, where d is the tens digit and 3 is the units digit.
10d + 3 must be divisible by d. So only d=3 satisfies this condition. SUFFICIENT.

(2) d is a factor of the two digit number d9, where d is the tens digit and 9 is the units digit.
10d + 9 must be divisible by d. Here, d=3 and d=9 satisfy the condition. INSUFFICIENT.

ANSWER A