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

1 < 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.

23
33
43
53
63
73
83
93

d is equal to 3. Sufficient.

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

29
39
49
59
69
79
89
99

d can be 3 or 9. Not sufficient.

IMO A

The answer is D
As per statement A-D needs to be divisible by d where d is the tens digit and 3 is the units digit. 23,33,43,53,63,73,83,93. Amongst these numbers 33 is divisible by 3. The rest of the numbers are either prime or are not divisible by d
As per Statement 2- d9 needs to be divisible by d where d is the tens digit and 9 is the units digit. 29,39,49,59,69,79,89,99. Amongst these numbers 39 is divisible by 3. The rest are prime or are not divisible by d.
Hence Both statements are sufficient on their own. So, D

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

Statement 1 alone :
d3 - two-digit numbers can be: 33, 63, or 93
factors of two-digit numbers: 33 (3 x 11), 63 (9 x 7) 0r 93 (3 x 31)
so the values of d can be 3, 9, 7 so statement 1 alone is not sufficient to answer the question.

Statement 2 alone
d9 - two-digit numbers can be: 39, 69, or 99
factors of two-digit numbers: 39 (3 x 13), 69 (3 x 23) 0r 99 (9 x 11)
so the values of d can be 3, or 9 so statement 2 alone is not sufficient to answer the question.

Combination of (1+2)
d3, d9 so two-digit numbers can be (33, 39) or (63, 69)
so the factors of two-digit number (11, 3) (13,3) (9,7) (3,23)

So statement 1+2 is also not sufficient to answer the question.

Correct answer is E

Given: d is a single digit number > 1

To find: value of d

d could be a number between 2-9

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

According to statement 1,
d could be 3,6,7 and 9.

If d3=33,3 is a factor of 33.
If d3=63, 3, 7 and 9 are factors of 63.
If d3=93,3 is a factor of 93.


Statement 1 is not sufficient as we have multiple values for d.


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

According to statement 2, d could be 3,4,7 and 9.

If d9=39,3 is a factor of 39.
If d9=49, 7 is a factor of 49.
If d9=99, 3 and 9 are factors of 99.


We have multiple values for d so statement 2 is not sufficient.

Combining statements 1 and 2, is still not sufficient

so the answer is E , Neither of the statements are together sufficient.

Posted from my mobile device

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.