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17 May 2018, 01:43
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[GMAT math practice question]
In a certain theater, the first row has 12 seats, and each row has 1 more seat than the previous row. If the last row has 50 seats, what is the total number of seats in the theater?
A. 1003
B. 1029
C. 1129
D. 1209
E. 1,339
=>
The question asks for the value of 12 + 13 + ... + 50. This is the sum of an arithmetic sequence with first term a = 12, and last term l = 50.
The sum of n terms of an arithmetic sequence may be found using the formula n/2 (a + l).
The number of rows is n = 50 – 12 + 1 = 39.
So, the number of seats in the theater is 39 * ( 12 + 50 ) / 2 = 39 * 62 / 2 = 39 * 31 = 1209.
Therefore, the answer is D.
Answer: D
In a certain theater, the first row has 12 seats, and each row has 1 more seat than the previous row. If the last row has 50 seats, what is the total number of seats in the theater?
A. 1003
B. 1029
C. 1129
D. 1209
E. 1,339
=>
The question asks for the value of 12 + 13 + ... + 50. This is the sum of an arithmetic sequence with first term a = 12, and last term l = 50.
The sum of n terms of an arithmetic sequence may be found using the formula n/2 (a + l).
The number of rows is n = 50 – 12 + 1 = 39.
So, the number of seats in the theater is 39 * ( 12 + 50 ) / 2 = 39 * 62 / 2 = 39 * 31 = 1209.
Therefore, the answer is D.
Answer: D
18 May 2018, 01:48
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[GMAT math practice question]
If 10^n< 0.003456 <10^{n+1}, what is the value of the integer n?
A. -4
B. -3
C. -2
D. -1
E. 0
=>
When we multiply all sides of the inequality by 10^6, we obtain 10^{n*}10^6 < 3,456 < 10^{n+1*}10^6 or 10^{n+6} < 3,456 < 10^{n+7}..
Since 1,000 < 3,456 < 10,000, 10^{n+6}=1,000=10^3 and n+6=3. So, n=-3.
Therefore, the answer is B.
Answer: B
If 10^n< 0.003456 <10^{n+1}, what is the value of the integer n?
A. -4
B. -3
C. -2
D. -1
E. 0
=>
When we multiply all sides of the inequality by 10^6, we obtain 10^{n*}10^6 < 3,456 < 10^{n+1*}10^6 or 10^{n+6} < 3,456 < 10^{n+7}..
Since 1,000 < 3,456 < 10,000, 10^{n+6}=1,000=10^3 and n+6=3. So, n=-3.
Therefore, the answer is B.
Answer: B
20 May 2018, 18:14
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[GMAT math practice question]
How many 4-digit numbers have only even digits?
A. 500
B. 525
C. 600
D. 625
E. 800
=>
Suppoose abcd is 4-digit number with only even digits.
Then a is one of 2, 4, 6 and 8, and b, c and d may be selected from the digits 0, 2, 4, 6 and 8.
So, there are 4 choices for a, and 5 choices for each of b, c and d.
The total number of 4-digit numbers with only even digits is thus 4*5*5*5 = 500.
Therefore, A is the answer.
Answer: A
How many 4-digit numbers have only even digits?
A. 500
B. 525
C. 600
D. 625
E. 800
=>
Suppoose abcd is 4-digit number with only even digits.
Then a is one of 2, 4, 6 and 8, and b, c and d may be selected from the digits 0, 2, 4, 6 and 8.
So, there are 4 choices for a, and 5 choices for each of b, c and d.
The total number of 4-digit numbers with only even digits is thus 4*5*5*5 = 500.
Therefore, A is the answer.
Answer: A
