VTMO 2015 — Grade 5 — semifinal

Question 1

Which expression equals $17$? Printed choices: A $4 \times 5 + 6 \times 3$; $B 4 \times 5 + 6 \div 3$; $C 6 \div 3 + 5 \times 4$; $D 3 \times 4 \div 6 + 5$; $E 3 + 4 \times 5 \times 6$.

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Question 2

A rectangle has perimeter $42 \,\mathrm{cm}$ and width $4 \,\mathrm{cm}$. What is its length in cm?

$17$
$19$
$21$
$34$
$38$

Question 3

An’s birthday is Wednesday; Binh’s is $17$ days earlier. What weekday is Binh’s birthday?

Wednesday
Thursday
Friday
Saturday
Sunday

Question 4

Trung is $150 \,\mathrm{cm}$ tall and grows $5 \%$ by summer’s end. What is his new height?

$157$
$157.5$
$158$
$158.5$
$165$

Question 5

Define $a\otimes b=a\times b+a+b$; for example $8\otimes5=53$. Find $9\otimes3$.

$36$
$39$
$42$
$45$
$48$

Question 6

$N$ is two-digit, leaving remainder $9$ modulo $10$ and $8$ modulo $9$. Find its digit sum.

$8$
$9$
$10$
$16$
$17$

Question 7

A rectangle has area $48 \,\mathrm{cm}^{2}$, perimeter $32 \,\mathrm{cm}$, and natural-number side lengths. What is length minus width?

$4$
$6$
$8$
$10$
$12$

Question 8

Evaluate $(1+\frac12)(1+\frac13)(1+\frac14)(1+\frac15)$.

$3$
$\frac{7}{2}$
$4$
$\frac{9}{2}$
$6$

Question 9

Color each cube face with one color so adjacent faces have different colors. What is the minimum number of colors?

Question 10

All three balances are level as shown. How many times the square’s value is the circle’s value?

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Question 11

A bicycle’s rear-wheel diameter is $60 \,\mathrm{cm}$ and front-wheel diameter $50 \,\mathrm{cm}$. The rear wheel turns $700$ times. How many front-wheel turns occur?

$500$
$600$
$700$
$720$
$840$

Question 12

The mean of $101$ consecutive even integers is $198$. What is the sum of the smallest and largest?

$198$
$200$
$288$
$396$
$400$

Question 13

Each time Pi cuts one sheet into $4$ smaller sheets. After $7$ cuts there are $30$ sheets. How many were there initially?

$3$
$5$
$7$
$9$
$11$

Question 14

$A = 5 \times 5$ table has row sums $10 , 13 , 15 , 16 , 17$. Its first four column sums are $9 , 8 , 14 , 25$. Find column $5$’s sum.

Question illustration

$12$
$13$
$14$
$15$
$16$

Question 15

At $3 : 47$ the displayed digit sum is $14$. After at least how many minutes will the hour-and-minute digit sum be $20$?

$42$
$132$
$192$
$251$
$301$

Question 16

Rectangle $PQRS$ has $PS = 2 \,\mathrm{cm}$; $JKLM$ is a square of side $8 \,\mathrm{cm}$. Find the total shaded area.

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$16\text{ cm}^2$
$32\text{ cm}^2$
$48\text{ cm}^2$
$56\text{ cm}^2$
$62\text{ cm}^2$

Question 17

Pupils are evenly distributed among buses. One breaks down and its pupils are evenly reassigned to the other buses, adding $3$ to each and making $27$ on each. How many pupils are there?

$216$
$218$
$224$
$240$
$254$

Question 18

$P , Q$ are digits in $77 P + 6 QP + QQP = 1 PP = 7$. Find $P + Q$.

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$9$
$12$
$13$
$14$
$15$

Question 19

One of An, Binh, Chau and Dung breaks a window. An says “Binh did it”; Binh says “Dung did it”; Chau and Dung both say “Chau did not do it.” Who did it, given that exactly one person tells the truth?

Original choices: $A$. An; $B$. Binh; $C$. Chau; $D$. Dung; $E$. Insufficient information

Question 20

$A = 4 \times 4$ array of $16$ circles has $12$ black boundary circles. If $196$ circles form a square array, how many are on its boundary?

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$42$
$44$
$48$
$50$
$52$