GRE
Practice Test 11
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On Tuesday, Paul withdraws funds from his savings account equal to 15% of the amount of the deposits. On Thursday, he deposits $175. If there were no others transactions made by Paul and if the amount in the account, following Thursday’s transaction was 120% of the original amount, then how much money was originally in the account?

  • Solution

    Method 1:

    Since addition on Thursday is 35%, which is $175.

    ∴ Original amount on Monday is 100% which is - $500.

    Method 2:

    Let there be 100x dollars originally. After Tuesday's transaction, money in the account = 85x.

    After Thursday's transaction, money in the account = 120x

    ∴ 85x + 175 = 120x ∴ 35x= 175 ∴ x= 5

    ∴ The original sum in the account = $500

Find the least number which when divided by 6, 15, 17 leaves remainder 1, but when divided by 7 leaves no remainder.

  • Solution

    Number must be the LCM of 6, 15, 17 plus 1. LCM of 6, 15, 17 is 510.

    ∴ Number is 510 + 1 = 511. Incidentally 511 is also divisible by 7.

Pat spent $9.60 for fruits and vegetables that included apples, figs, tomatoes and carrots. Cost of the figs alone was equal to the cost of tomatoes and carrots combined. Cost of apples was $2.80. What was the cost of carrots?

  • Solution

    Let the cost of apples, figs, tomatoes and carrots be 'a', 'f, 't' and 'c' respectively.

    ∴ a + f + t + C = $9.60

    ∴ (t + c) + (t + c) = 9.60 - a

    ∴ 2(t + c) = 9.60 - 2.80 .. t + C = $6.80

    ∴ The total price of tomatoes and carrots is $6.80. But nothing can be said about the cost of carrots alone

In a staircase of four steps, Sally can jump one step, 2 steps, 3 steps or all 4 steps. In how many ways can she reach the top?

  • Solution

    Case I - Taking 1 step first

    (1, 1, 1, 1), (1, 1,2), (1, 2,1), (1,3)

    Case II - Taking 2 steps first (2, 1, 1), (2, 2)

    Case III - Taking 3 steps first (3, 1)

    Case IV - Taking 4 steps rust (4, 0)

    Total ways = 4 + 2 + 1 + 1= 8

A class of 80 students comprises girls and boys. Each boy contributed dollars equal to the number of girls and each girl contributed dollars equal to the number of boys. The total amount collected was $3000. How many boys could be in the class?

  • Solution

    Let number of boys and girls be 'b' and 'g' respectively.

    ∴ b + g = 80

    Now contribution made by each boy is 'g' and' that made by each girl is 'b'.

    ∴ 2bg = 3000

    ∴ bg = $1500 and b + g = 80

    ∴ b and g can have two values 30 or 50.

The price of a microchip declines by 66.67% every 6 months. At this rate, approximately how many years will it take for price of a $81 microchip to reach a price of $1?

  • Solution

    Price declines by 66.67%.

    ∴ New price is 33.33% i.e. 1⁄3 of old price.

    After 6 months, $81 is reduced to 1⁄3 of 81 = $27

    After 1 year, $27 goes down to $9

    After 1 1⁄2 years, $9 goes to $3

    ∴ After 2 years, it becomes $1

The ratio between the school ages of Neeta and Sameer is 5 : 6 respectively. If the ratio between the onethird age of Neeta and half of the Sameer’s age is 5 : 9 then what is the school age of Sameer?

  • Solution

    Since we do not have information about age of either Neeta or Sameer, it is difficult to find out the answer.

A man 182 cm tall decided to walk around the earth along the equator. The top of his head describes a circle whose circumference is greater than that described by his feet. What is difference between circumferences?

  • Solution

    Let r be radius of earth. Then circumference of circle described by feet = 2πT.

    Circumference described by top of head = 2π(r + 132)

    ∴ Difference = 2π(r+ 182)- 2πT.

    = 2π(r+ 182 - r)

    = 2π x 182 cm = 11.44 metres

What is the smallest number, which when divided by 10 leaves a remainder 9, when divided by 9 leaves a remainder 8, when divided by 8 leaves a remainder 7 and so on till divided by 2 leaving a remainder 1.

  • Solution

    The number must be of the form n - 1, when n is the LCM of 2,3,4,5,6,7,8,9. The LCM is 2520.

    ∴ The number must be 2519.

Tom, Dick and Harry join a 1500 meters running race. Tom beats Dick by 100 meters and Harry by 150 meters. By how many meters does Dick beat Harry over full distance?

  • Solution

    When Tom runs 1500 meters, Dick and Harry run 1400 meters and 1350 meters respectively.

    ∴ In a race of 1400 meters, Dick will beat Harry by 50 meters. But the actual race is of 1500 meters.

    ∴ Dick will beat Harry by

    \(\frac{1500 \times 50}{1400}\)= 534⁄7 meters.

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